{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Crafting summary statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many simulators produce outputs that are high-dimesional. For example, a simulator might generate a time series or an image. In a [previous tutorial](https://sbi-dev.github.io/sbi/tutorial/05_embedding_net/), we discussed how a neural networks can be used to learn summary statistics from such data. In this notebook, we will instead focus on hand-crafting summary statistics. We demonstrate that the choice of summary statistics can be crucial for the performance of the inference algorithm.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "\n",
    "# sbi\n",
    "import sbi.utils as utils\n",
    "from sbi.inference.base import infer\n",
    "from sbi.inference import SNPE, prepare_for_sbi, simulate_for_sbi\n",
    "from sbi.utils.get_nn_models import posterior_nn\n",
    "from sbi.analysis import pairplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# remove top and right axis from plots\n",
    "mpl.rcParams[\"axes.spines.right\"] = False\n",
    "mpl.rcParams[\"axes.spines.top\"] = False"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook is not intended to provide a one-fits-all approach. In fact it argues against this: it argues for the user to carefully construct their summary statistics to (i) further help the user understand his observed data, (ii) help them understand exactly what they want the model to recover from the observation and (iii) help the inference framework itself."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 1: The quadratic function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assume we have a simulator that is given by a quadratic function:\n",
    "\n",
    "$x(t) = a\\cdot t^2 + b\\cdot t + c + \\epsilon$,\n",
    "\n",
    "where $\\epsilon$ is Gaussian observation noise and $\\theta = \\{a, b, c\\}$ are the parameters. Given an observed quadratic function $x_o$, we would like to recover the posterior over parameters $a_o$, $b_o$ and $c_o$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 Prior over parameters "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we define a prior distribution over parameters $a$, $b$ and $c$. Here, we use a uniform prior for $a$, $b$ and $c$ to go from $-1$ to $1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "prior_min = [-1, -1, -1]\n",
    "prior_max = [1, 1, 1]\n",
    "prior = utils.torchutils.BoxUniform(\n",
    "    low=torch.as_tensor(prior_min), high=torch.as_tensor(prior_max)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 Simulator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Defining some helper functions first:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_t_x(theta, seed=None):\n",
    "    \"\"\"Return an t, x array for plotting based on params\"\"\"\n",
    "    if theta.ndim == 1:\n",
    "        theta = theta[np.newaxis, :]\n",
    "\n",
    "    if seed is not None:\n",
    "        rng = np.random.RandomState(seed)\n",
    "    else:\n",
    "        rng = np.random.RandomState()\n",
    "\n",
    "    t = np.linspace(-1, 1, 200)\n",
    "    ts = np.repeat(t[:, np.newaxis], theta.shape[0], axis=1)\n",
    "    x = (\n",
    "        theta[:, 0] * ts**2\n",
    "        + theta[:, 1] * ts\n",
    "        + theta[:, 2]\n",
    "        + 0.01 * rng.randn(ts.shape[0], theta.shape[0])\n",
    "    )\n",
    "    return t, x\n",
    "\n",
    "\n",
    "def eval(theta, t, seed=None):\n",
    "    \"\"\"Evaluate the quadratic function at `t`\"\"\"\n",
    "\n",
    "    if theta.ndim == 1:\n",
    "        theta = theta[np.newaxis, :]\n",
    "\n",
    "    if seed is not None:\n",
    "        rng = np.random.RandomState(seed)\n",
    "    else:\n",
    "        rng = np.random.RandomState()\n",
    "\n",
    "    return theta[:, 0] * t**2 + theta[:, 1] * t + theta[:, 2] + 0.01 * rng.randn(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we generate the observation $x_o$ from parameters $\\theta_o=(a_o, b_o, c_o)=(0.3, -0.2, -0.1)$. The observation as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f828b191d60>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta_o = np.array([0.3, -0.2, -0.1])\n",
    "t, x = create_t_x(theta_o)\n",
    "plt.plot(t, x, \"k\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.3 Summary statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will compare two methods for defining summary statistics. One method uses three summary statistics which are function evaluations at three points in time. The other method uses a single summary statistic: the mean squared error between the observed and the simulated trace. In the second case, one then tries to obtain the posterior $p(\\theta | 0)$, i.e. the error being zero. These two methods are implemented below:\n",
    "<br>\n",
    "$\\textbf{get_3_values()}$ returns 3 function evaluations at $x=-0.5, x=0$ and $x=0.75$.\n",
    "<br>\n",
    "$\\textbf{get_MSE()}$ returns the mean squared error between true and a quadratic function corresponding to a prior distributions sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_3_values(theta, seed=None):\n",
    "    \"\"\"\n",
    "    Return 3 'y' values corresponding to x=-0.5,0,0.75 as summary statistic vector\n",
    "    \"\"\"\n",
    "    return np.array(\n",
    "        [\n",
    "            eval(theta, -0.5, seed=seed),\n",
    "            eval(theta, 0, seed=seed),\n",
    "            eval(theta, 0.75, seed=seed),\n",
    "        ]\n",
    "    ).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_MSE(theta, theta_o, seed=None):\n",
    "    \"\"\"\n",
    "    Return the mean-squared error (MSE) i.e. Euclidean distance from the observation function\n",
    "    \"\"\"\n",
    "    _, y = create_t_x(theta_o, seed=seed)  # truth\n",
    "    _, y_ = create_t_x(theta, seed=seed)  # simulations\n",
    "    return np.mean(np.square(y_ - y), axis=0, keepdims=True).T  # MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try a couple of samples from our prior and see their summary statistics. Notice that these indeed change in small amounts every time you rerun it due to the noise, except if you set the seed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.4 Simulating data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us see various plots of prior samples and their summary statistics versus the truth, i.e. our artificial observation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8289154eb0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t, x_truth = create_t_x(theta_o)\n",
    "plt.plot(t, x_truth, \"k\", zorder=1, label=\"truth\")\n",
    "n_samples = 100\n",
    "theta = prior.sample((n_samples,))\n",
    "t, x = create_t_x(theta.numpy())\n",
    "plt.plot(t, x, \"grey\", zorder=0)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In summary, we defined reasonable summary statistics and, a priori, there might be an appararent reason why one method would be better than another. When we do inference, we'd like our posterior to focus around parameter samples that have their simulated MSE very close to 0 (i.e. the truth MSE summary statistic) or their 3 extracted $(t, x)$ coordinates to be the truthful ones."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.5 Inference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.5.1 Using the MSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if we can use the MSE to recover the true observation parameters $\\theta_o=(a_0,b_0,c_0)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = prior.sample((1000,))\n",
    "x = get_MSE(theta.numpy(), theta_o)\n",
    "\n",
    "theta = torch.as_tensor(theta, dtype=torch.float32)\n",
    "x = torch.as_tensor(x, dtype=torch.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Neural network successfully converged after 181 epochs."
     ]
    }
   ],
   "source": [
    "inference = SNPE(prior)\n",
    "_ = inference.append_simulations(theta, x).train()\n",
    "posterior = inference.build_posterior()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've build the posterior as such, we can see how likely it finds certain parameters given that we tell it that we've observed a certain summary statistic (in this case the MSE). We can then sample from it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7eacd39b7c664233a46a5081416ae57d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Drawing 10000 posterior samples:   0%|          | 0/10000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_o = torch.as_tensor(\n",
    "    [\n",
    "        [\n",
    "            0.0,\n",
    "        ]\n",
    "    ]\n",
    ")\n",
    "theta_p = posterior.sample((10000,), x=x_o)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = pairplot(\n",
    "    theta_p,\n",
    "    limits=list(zip(prior_min, prior_max)),\n",
    "    ticks=list(zip(prior_min, prior_max)),\n",
    "    figsize=(7, 7),\n",
    "    labels=[\"a\", \"b\", \"c\"],\n",
    "    points_offdiag={\"markersize\": 6},\n",
    "    points_colors=\"r\",\n",
    "    points=theta_o,\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior seems to pretty broad: i.e. it is not so certain about the 'true' parameters (here showcased in red)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1ab62e5ca8c4439dae0b3a65bdf33db9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Drawing 10 posterior samples:   0%|          | 0/10 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f82882cd670>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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URdatW8eRI0dobm7u9bEWLlyIl5cXgiBw586d+zx1FAoFLi4ucsCXkZH50XkuAz50aePnzZuHUqlEpVJx+/ZtPvvss15vWiIIApMnT0YQBDo6Oh7YE7c7j3/+/PmndrchIyMj8308twEfunrUTpgwgcbGRsaNG4coipw7d67Xx7GwsGD69OkAREVF3Vf0FRwcjJ+fH5cuXWL37t2yuZqMjMyPwnMd8AFCQkJwcnLi0qVLWFhYkJWV9VQUM4MGDcLBwYGGhgY+/fRT4uLipOf09fVZsGAB06dPJy8vj4SEhF4fX0ZGRub7eO4DvkKhYP78+fTr10+qvL1z5w5arbbXV9rz588HwMjIiPj4+PuKvoKCgujbty9RUVHU1tb26tgyMjLPB9nZ2U9NXfjcB3zokmq+9NJLDBo0CIDLly/z0UcfcebMmV4dx8LCAj8/P9ra2qioqOD//u//qK+vl57vbo+oUCjYt2+f3DRFRkbmPi5cuPBUUs/wggT8boYMGQJAS0sLxsbGxMfH09DQ0KtjDB8+XKq87ejo4PDhw1RVVUnPm5ubM3v2bMrKyti3bx91dXW9Or6MjMzPl/b2doqLi3F3d38q53+hAr69vT0ODg5YWVmxdOlStFotV65c6dUxHB0dCQ8Px8rKCkEQyM/PZ+vWrT32Dby9vZk8eTK5ubls2LCh10zeZGRkft4UFBQgiqIc8HuLkJAQqqurKS0tJSAggISEhF6zUu4mNDSU4OBgtFotKpWK1tZWDhw40MNzZ+jQobzzzjsYGhpy9OhROb0jIyNDbm4uSqUSJyenp3L+Fy7gDxgwABsbG86ePcuoUaNQqVTs3btX0sdXVFRw/fp1Lly4IHWwehxCQ0N5//33mTx5MqIokp+fz7Fjx3psFJuZmTF9+nSqqqq4fPnyE783GRmZnze5ubk4Ozujo6PzVM7fKwFfEITJgiBkCIKQJQjCb77juHmCIIiCIAzujXEfB4VCQVhYGDU1NeTm5jJ//nwqKyvZvn07586d4/PPPyciIoKLFy/eZ338QxAEATMzMwYNGoSNjQ36+vrcunWLmJiYHsd5enoyYMAAYmNj5Xy+jMwLTENDA2VlZU8tnQO9EPAFQVACG4ApgB+wWBAEvwccZwK8BzyTFlCiKD5Udunl5YWLiwsXLlzA2dmZuXPn0tjYyOXLl+nXrx+/+MUvsLS0JCUl5YnnoVAoCA8Pp62tDQsLC65evXpf+mbChAkIgsDZs2efeDwZGZmfH4mJiaxfvx5BEPD29n5q4/TGCj8EyBJFMUcUxQ5gDzDrAcf9N/AR0NYLY34v0dHR/OUvf+HYsWP3rZwFQWDChAk0Nzdz9epV/P39effdd1m+fDmLFi3C1NSU/v37k5ub2yv+Ox4eHgQGBlJbW0trays7duygvb1det7U1JThw4dz584dtm/fLhdmyci8QGi1WqKjo7G1tWX16tXY2dk9tbF6I+A7AoX3/F70r8ckBEEIApxFUTz5XScSBGGVIAjxgiDEV1ZWPvaESktL2b9/Pzk5Ody5c4evvvqKb5/P2dkZX19frly5QnZ2Njo6Ori6uiIIAgD9+/dHFEVSU1Mfex73Eh4ejomJCQCFhYXcunWrx/MjR44kNDSUlpYWTpw4QWZmZq+MKyMj89OmpKSE1tZWQkNDsbGxeapjPfVNW0EQFMA/gF9937GiKG4WRXGwKIqDH/eNq9VqVq9ezZdffsmXX37JqFGj0Gq1bNmyhRMnTvRQ5EyaNAlTU1N27tzZwwoBwNbWFhsbG6Kjozl8+DAtLS2PNZ9u9PX1Wb16NePHjwfgzJkzXLx4UVLu6OjoEB4ezhtvvIGtrS1HjhyRc/oyMi8AmZmZCIKAh4fHUx+rNwJ+MeB8z+9O/3qsGxPAH7ggCEIeEAoce1obt4mJiZw8eZKwsDD09fXZsWMHK1euxMPDg7/+9a/8x3/8BxcuXECtVmNubs6qVatwdHS8L40iCALz58/Hz8+PlJQUjh8/Lu0JaDSaHimZR8XAwIARI0bg6+uLRqPhwoULbNiwgXPnzpGVlQWASqVi/vz5qNVqPv/8czIyMp78Q5GRkfnJ0dnZiVqtJisrCycnJwwMDJ76mL0R8OMAT0EQ3AVB0AUWAce6nxRFsV4URWtRFN1EUXQDrgEzRVGMf/DpnoyQkBBu3rxJREQEy5cvZ8eOHVy/fp2NGzdy6dIloqOjuXDhAhs3bqSkpAQdHR28vLwoLy+/bxVva2vLrFmzGD9+POnp6Vy7do2ioiI+++wzNm3a1ENX/6goFAqmTZuGQtH10dfW1nL58mUOHjwoXURsbGx48803sbCwYP/+/VRXVz/5ByMjI/OTYuvWraxbt46SkhL69ev3TMZ84oAviqIaeAc4A6QB+0RRTBEE4Y+CIMx80vM/Dv7+/igUCn75y1+iVquZMmUKsbGxzJs3j5ycHHx8fOjs7JS8dLplUA9rQxgaGoqrqyuRkZF8+eWXNDQ0UF9fT1pa2mPNz8jIiJEjR9K/f39MTU2xt7enra2tx12GpaUlo0aNQhAETp48KVsqy8g8R9TV1VFaWopCoUChUODj4/NMxlX1xklEUTwFnPrWY797yLFje2PMR8HT05OrV69SX1+Pl5cXNjY2nD9/nr179/LBBx8QHR1NVVUVDg4OqFQq7t69i6+v733nUSgULF26lPz8fGpqavDx8WHr1q3ExcXh7+//WHMbN24c8O9+uM7Ozly7do2QkBBUqq4/y9WrV9FqteTm5nLjxg2GDh36+B+GjIzMT4bs7GwAXnnlFUxNTdHT03sm4z73lbYhISFMnDgRV1dXDA0NWb16NUeOHOHChQsA3Lx5UypnTkpKIiUlhcLCQrZv397DwlilUuHh4cGQIUMwMTFh8ODBFBQUUFZW9kTz8/PzQxRF7O3taWxs5MyZM4iiSEtLC4WFhWi1Wtzc3IiIiCAxMfGJxpKRkflpkJ2djampKdbW1s8s2EMvrfB/Tvz2t7/l7t27/Nd//Rfe3t4kJCQQFBSEnp4eBQUFHD16FKVSSVtbGzExMcyYMeOB5xk0aBDnzp0jKSmJyZMnP/Z87O3tMTU15caNGwDEx8cjCAKOjv9WtgYHB6NUKjl+/DiNjY2MHj1ako/KyMj8vNBqteTk5ODn5/fM/4+f+xX+tzEwMGDPnj38/e9/R6vVcvz4cQRBoKqqiq+++oqcnBwEQcDHx4fk5OSHdscyMDDA09OTlJSU+xqd/BAEQWD69OmMGjWKSZMmoVQqiYuL49q1axgaGgJQXV3NokWLGDhwIBcuXJB9d2Rkfsbk5eXR3t7+zDZq7+WFW+ED0obu+++/z7Bhw/j0008lX/zi4mL8/f0JCwsjPT2dyMhIxowZg5WV1X3nGTBgAOnp6aSlpZGUlER5eTlGRkasXLlSysM/Cp6ennh6egJdfvn79u2jrKyMoKAgcnNzqaioQKVSMWvWLDo7O7l8+TL+/v4UFhaSnZ1NZ2cn8+bN+0FjysjIPHsqKio4ePAgJiYmz0R3/21e6AihUCjYtGkTQ4YMwcLCAhsbG8rLy6mvr6euro7BgwcTHx/P7du36du3L+PGjethW+rp6Ymenh4HDx5EoVDg5eVFWload+7cITAw8LHm5OPjg7GxMR0dHQwaNIjm5mYqKiqArruB8PBwMjMz+eyzz+js7MTQ0JCWlpYnGlNGRubp09LSwtdff41SqWTZsmXPNHffzQuX0vk2QUFB7N27l+PHjzNnzhxu374tpVWmTZvGe++9R1hYGOXl5WzdupX4+H+XD+jo6ODn1+UTt2DBAhYsWICtrS3Xrl17bBmlIAgEBgbS2dnJsWPHKCgooLq6WjJcMzU1ZeLEiRgZGTF37lw++OADbGxsuH79uizdlJH5iSKKIseOHaO1tZWXX375gRmDZ8ELH/Chq/n4sGHDmDBhAmq1GkEQuHv3LsXFxZiamjJy5Ejeffdd+vbty8mTJ3vo5adMmcLbb7+Nt7c3giAQEhJCeXn5EzUhDgwMRBAERFGktbUVURR7tEl0cHDA398ff39/BEFg6NChlJWVUVBQ8ESfg4yMzNMhISGBjIwMJkyYQJ8+fX60ecgB/x6GDx+OgYEBW7duZcOGDbi4uDB8+HAqKyvR1dVl8eLF9O3blzNnzkjVrzo6Oj2u1gEBAZiYmLBnzx6io6PZt28f6enpP2geVlZW/OpXv2LNmjX0798fQJJkarVajhw5QkxMjCQbDQgIwMDAgAsXLsirfBmZnxiVlZWcOXMGDw+PH72WRg7496Cvr8+qVavQ19dnyJAh+Pv7c/36dd58803S0tJQKBTMmjULpVIpmbMlJib2CLI6Ojq8/vrrODk5ERsbS3p6OrGxsQCkp6dTXFz8sOF7YGhoKCl47lXuXLt2TVrt5+TkSGOOHz+evLy8+1w4ZWRkfjxEUeTIkSPo6uoye/bsH11OLQf8b7Fu3Tru3LnDyZMniYyMpH///pw9e5YvvviCuro6TE1NWbRoER4eHqjVao4fP86uXbt6BH1TU1NeeeUVPvzwQ0aNGkVxcTF1dXUcPHhQsnN4VPT19Zk0aRLQ5bAZFRUl+fDcuXNHOi44OBhnZ2fOnDlDXl7ek38QMjIyT0xNTQ0lJSWMHj0aY2PjH3s6csD/Luzs7Pjyyy9pb29n3bp1DBgwgLq6OlxdXZk3bx6rVq1i3LhxZGVlSW6X3QiCgKGhIZ6enoiiyIkTJ1Cr1RQVFdHa2kpeXp60Qv8+Bg8ejJWVFQYGBlhYWKDValEoFBQVFREfH8/HH39Me3s7M2fORF9fn+3bt3PlypWn8ZHIyMj8ALr/x38Mzf2DkAP+9zB06FDy8vJYsmQJJSUlvPHGG6xZs4bFixfT3t7OiBEjMDU15cqVK2RmZhIdHd3DRdPBwQEDAwOys7PR1dWVmqrs2bOHr7/+mlOnTn1v4ZZCoWDOnDlYWFhQW1vLkCFDcHFxQaPRcPr0aRoaGrh79y7W1tasXr0aT09PLl68SGtr69P+eGRkZL6DnJwczMzMsLS0/LGnAjyHOnxRFImOjmbEiBFSpeqT0qdPH1auXElxcTEHDhxApVKhVqvRaDTs2bOH0NBQIiMjpVRKS0sLnp6eFBcXM2bMGDw8PLhz5w7Dhw/n+vXrREVF0d7ejp+fH3Fxcbi7uz/QtO1eHB0deeONN6S0UmZmJnl5eSgUCgwMDEhLSyMgIAAdHR3CwsL47LPPuHHjBmPGjOmVz0BGRuaH0W18+GNYKDyM5y7gZ2dnc+XKFRISEnjttdewtbXtlfOOHTuWjo4OjIyMGDJkCB0dHfzP//wP48ePZ8WKFSQlJeHs7Iyenh5Xrlzh5s2bQFdlXbfPft++famsrCQlJQU3Nzfmzp1LTk7OQ106H4S5uTnQ1YjdzMyM+vp6HB0dycrKoqOjA11dXezs7PD29ub69esMGzYMXV3dXvkMZGRkvp+mpiYOHTqErq4u7e3tP0pF7cN47lI6Hh4eBAcH097ezubNm+no6OiV83ZXuX700UeYmZlhYmJCYGAgW7ZsQU9Pj9WrVzN9+nSGDx9OaWkp/v7+TJs2jczMTEpLSwEoKyvDyMgIADc3N5RKJR4eHmRmZv5gOaUgCLzzzjt4enqSn5+PWq3u0Qd35MiRtLa2yg3RZWSeIU1NTWzfvp3CwkKysrJQKBRSv42fAs/dCr9byghdxQ7R0dFMnTq1187fv39/BEFg//79zJw5kz/+8Y/Ex8ezd+9e6urqiI2NJS0tjbt373Lu3DnMzc0xNTVl9+7dPTZ2U1JSGDVqFF5eXqSkpFBaWoqDg8MPmotKpWLOnDmsW7cOrVYrbQwPHDgQJycn3NzcuHr1KkOGDJF9dmRknjJZWVkcPXqU9vZ2li5dirW1NU1NTb2WWu4Nnsso0N3lKikpicTERCZNmtSrAa9v374oFAr69++PSqViwoQJ1NfXY2dnh5GREQsWLGD//v3cvXsXLy8voGuXPjk5GY1GQ58+fSgrKyM+Pl6qls3IyOgR8CsqKrCxsfne3F93n9zz58+jq6vLkSNHKCsrIzg4GAcHB/Ly8khOTiY4OLjX3r+MjExP6uvr2b17N9bW1ixduhQ7OzsA6Y7+u1Cr1Zw6dYrs7Gxpwfq0VD3PXUqnvr6ejRs3kpaWRmBgIBqNhpMnT/bqGPr6+ri4uFBVVcX06dOpr6/n008/paysjOzsbP75z3+iUqn44osvpNf069ePzs5OtFot06dPlyp2CwoKcHFxITY2lhMnTlBXV8fFixfZtGkTMTExjzSfoUOHYmxsLPXEvXbtGhs2bODKlStYWVlx9uxZ6uvruX79utxERUbmKZCamopWq2XhwoVSsH8U2tvb2b17Nzdv3pT2APfs2XOfzLu3EH6qpfiDBw8W7zUqe1Q6Ozv55ptvKCwsxMvLS7I1mDFjBm1tbVRVVdHa2srcuXPR0dF57PnFxsYSHR3Nyy+/TG5urlQc1c38+fO5cOECBQUFGBoa0tHRwf/93/9hamrKu+++S3t7O9988w0lJSUsWrSIjIwMkpKS0Gq1iKKIrq4uCoWC9957D319/e+dT2trK0qlkt27d1NaWsqIESOIiYnBw8OD7OxsFAoFbW1tKBQK3nnnHSwsLB77vcvIyPRky5YtaLVaVq1a9civKSsrY//+/dTW1jJz5kwCAwNpbW1lx44diKLIqlWrpCLLH8hD0wLP3QpfR0eHxYsXY29vT3p6OkqlEoDjx48TFRXFzZs3SU9PZ8uWLTQ3Nz/2ON3+9dXV1fcFe4D333+f6upq1q9fD4Curi7jxo0jLCwMQRDQ19dnyZIl6OvrExsbS2hoKO7u7gQEBBAaGsqyZctoa2vj6tWrjzQfAwMDdHV1GT58OO3t7VKDlvz8fGbMmEFnZyfDhw9HoVBw/vz5x37fMjIyXXRX2sfFxVFcXCw55z4KFRUVbNu2jc7OTpYtWyZZmxsYGPDKK6+wZMmSxw3238lzF/AB9PT0WLZsGWvXrmXs2LHS4/fm06qqqoiKinrsMWxsbKRUzIOUQCNHjmTatGn85S9/kUzORowYIZmhQVdqaOzYseTn57NlyxaysrKoqqpi4sSJ2NvbY2ZmxuXLl6mtrUUURcki+bvo168f9vb2nDx5krKyMlpaWjAxMeE3v/kNEydOJDQ0lNu3bz9xL14ZmRedkpISEhMTOXXqFECP/+3vorm5mV27dqGjo8Nrr72Gq6trj+cNDQ0xMTHp9fnCcxrwoWulb2FhgY+PD9BV8drc3IyBgQH29vbo6emRkZHBsWPHpNz3D0EQBMLCwmhqauLcuXOkpqbS1tbW45j/+Z//ob6+nqCgIFasWEFjY+N95wkKCsLKygpBEBg9ejTFxcWcPXuWy5cvU19fjyiKfPPNN+zevZt169Y9tOXivfNavnw5U6ZMoba2FkEQSE1NRaVSIYoiw4cPR19fn7Nnz/7g9ywjI/NvysvLgS7rk6FDhz5ymjQ+Pp76+noWL14s1dU8K3pFuiIIwmTgE0AJbBFF8X+/9fwvgdcBNVAJvCaKYn5vjP19WFtbY2VlJbUwbG1tRavVSkH+5s2bKJVKRo0ahamp6Q86t4uLC15eXly/fl0qcro3vRMQEMD27ds5dOgQO3bsoKGhgZdffpkNGzZgY2PDqlWrCAsLY/ny5YiiiLGxMRUVFZIPjre3N/X19ZSVlVFdXY0gCBw/fhwjIyMKCgpYsWLFA1UAurq6hISEoFariYqK4saNG2RlZaGnp4euri4jR44kOjqavLw83NzcHvOTlZF5sSkvL0dfX5+pU6f+oEra9PR0nJ2df7AMuzd44k1bQRCUwF1gIlAExAGLRVFMveeYccB1URRbBEFYDYwVRXHhd533cTdtH8T58+e5dOkSAQEB9OnTh7Nnz0p+NwYGBrS2ttK3b19eeeWVH3zu1tZWioqKiImJoaWlhbfffvuBx/3973/ngw8+ALqKwxobG9FoNOTl5fVw0dNqtZSXl1NRUYGPjw8dHR189tlntLS0SHOFLn8dT09PRowYQUVFBUFBQfd96bRaLbt27SInJ6dHYdeECRO4ceMGurq6vPTSS1y/fp22tjbmz5//g9+/jMyLyldffYVCoWD58uWP/Jra2lr++c9/MnHiRIYPH/60pvbQq09vrPBDgCxRFHMABEHYA8wCpIAviuK9u4TXgKW9MO4jM3r0aAIDA6VbLo1Gw9mzZ9HT05Py7zk5ObS2thIdHY2Ojg7t7e1MmjQJAwOD7zx39+ZodXU1Z86coba29oG3dr/85S+pra3FyMiIDz74gISEBIYNG8bGjRv59a9/LR2nUCiwt7fH3t4e6NqP+PDDD8nIyGDPnj307duX4cOHU1FRQWRkJBkZGQBYWlri5uZGc3OzdAFRKBQsXbqUrKws9u3bR2dnJ46Ojly8eJGQkBCuXbvGxo0bpbEnTpyImZnZE3zSMjIvBqIoUl5ezsCBA7/32NTUVDIyMmhvb5dy892p5mdNbwR8R6Dwnt+LgO9q67ISOP2gJwRBWAWsgq50yeNSUVHBpUuXKC8vx83NjeDg4B5txYYPH05hYSF3797t8bqPP/6Yzs5O6XdnZ2eCgoIeaUwvLy/OnDnD3bt3H9jVRhAE/vSnP0m/h4aGMmnSJP72t7+xZs0aKUg3NjbS2tp6nweQt7c37u7ulJeX4+zsTN++fWlqasLIyIiYmBjOnz+Pvb09cXFxvPLKKz3Kufv168cHH3zAhg0bqKqqQhAEqSkLIDVCz87OfuT3KyPzIlNXV0dHR8f3au4zMjLYv38/RkZGaDQa2trasLW1/dHcM5/ppq0gCEuBwcBfH/S8KIqbRVEcLIriYBsbm8cao7q6mk2bNpGZmYmZmRnJycl8/vnnRERESGkNhULB4sWLefvttxk5ciSrV68G6BHsoevK/KhYWlpiZWXVw8/m+/jDH/5AVVUVixcvRq1Wk56eTkBAAB4eHuzdu/e+48eNG0dzc7Okte++LfT19aWwsJAbN25I3vvffi+6urq8/PLLODk50dHRga2tLbq6uhgZGUnpouzs7Eeeu4zMi0xFRQXAdwb8qqoqjh49Sp8+fXj//fdZs2YNAQEBjB49+qGv+T6r9CelN1b4xYDzPb87/euxHgiCMAH4LTBGFMUfLot5RKysrJgxYwY+Pj4YGhrS2tpKREQE169fZ/DgwVhbW0vHWltbExYWBnTZD3+7/WB+fj6iKCIIAkVFRbS0tEhWCQ+iewM3MzNT0ul/F6GhoWzYsIE1a9bg7e1NeXk5RkZG+Pn5sWjRIgRB4KWXXiI/Px9HR0ecnZ2ZNm0a586d44svvsDW1pZhw4ZJ/XUBwsPDOXPmDH//+98lTW/3asLOzo6lS5fS1taGnp4eRUVF7NixA+jai8jKypKaq8jIyNyPVqulpqZGamzSfSeu0Wg4duwYZWVldHZ2YmBgQElJCXp6esyfPx+VSoWJiQlz5sx54HmTkpK4cuUK1dXVknz6adAb/9lxgKcgCO6CIOgCi4Bj9x4gCMIg4HNgpiiKFb0w5ncSFBQkGRYZGBgwfvx4gPtSOPdyb4AWBEHyvM/Pz6e+vp6dO3eyb98+6urqHnqOkSNHYmtry549e8jNzX2kua5evZoNGzbQv39/Xn75Za5evUpMTAwDBw7kt7/9LdHR0fTt21cq4Bo8eDBr165lypQpKJVKjh49Sn5+Pr6+viiVSpKSkqRzNzc3P7Clor6+PoIg4OzszAcffCCtODo6Oti6dSsXLlx4pLnLyLxIxMbG8r//+79s2LCBGzduYGVlJVmPZ2ZmcuvWLYyMjHB0dERXV5dRo0bx9ttvY2Vl9Z3nLSws5NixY6hUKtzc3Dhz5gznz5//wQ66j0KvWCsIgjAVWEeXLPMrURT/LAjCH4F4URSPCYIQDQwASv/1kgJRFGd+1zl7U6UDsGnTJgwNDVm2bJn0mCiKtLa2YmhoSG1tLWfOnMHW1pbGxkYpcHbvJZSVlaHVavH19WXu3LkPHae1tZVNmzbh4ODAokWLHnu+x44dY9asWejp6dHe3k5wcDDf/jxEUeTWrVsUFRUxefJkjh07Jn3pmpubGTx4MPHx8SxZsuR7zZiio6N75PVnzpzJoEGDALh8+TLu7u44OTk99vuRkfk509nZyd/+9jfs7OwIDg5GT0+vRy5+9+7dlJSU8Itf/OIH3SF3q/BEUeStt95CR0eH48eP09HRwbx583rdWqFXdPiiKJ4CTn3rsd/d8/OE3hjnSfDy8iI2Npa2tjZ0dXVJSUkhJiaGqqoqXnvtNZqbmykoKGDixIlYWlqio6NDXFwcBQUFQNdGr0aj4fr160BX0/BvV8hB1x2Ft7c3ycnJqNXqx3bpnDFjBkOGDCEpKYmlS5eyc+dOsrKycHd35+bNm7S2tjJq1CgGDhwoKQXGjBkj6ew3bNiAWq3G0tKSkydPsmrVqh6Ko5aWFtRqtVR7MGHCBGpra6V9i+PHj5OZmYmdnR0XLlzA399fDvgyLyx3796lo6ODsWPH0rdv3x7PNTQ0kJmZyYgRI35wgL516xa1tbUsW7YMPT09oGux9bRSq8+lPfKD8PLyIiYmhkOHDlFdXU1NTQ3W1tYYGBhw/PhxmpubaW1t5caNG0yZMoWpU6eiVqtJTk5GFEVyc3MlCeft27e5ffs2oaGhhIWF3RfUPT09iY+PJz8//7G73QiCwLFjxygsLKRPnz7s3LmT//qv/+LKlSsUFhYiCAJpaWl4e3tLr7G0tGTatGlAV5l3amoqU6dO5ejRo3zxxReYm5tjbGyMra0t165dQ6vV8uabb0pSzKlTp0r7Fi0tLWRkZJCWlgbw1Nz7ZGR+Dty+fRtDQ0MphRMZGUlxcTHBwcGkpaUhiqJ0R/xDyMjIwMLCosfiURAEyQOst3lhduccHR2xtramqKgIExMTFixYwJo1a5gyZQrl5eU0Nzfj5OREUlKSVIU7c+ZMFi5ciCiKlJaW0tDQ0KOS9tq1axw/fvy+sdzd3VEqlT9IsfMg+vTpw5AhQ3B2dmbEiBHs3bsXXV1dqcvWX//6QLETgCQNPXLkCKIoUltbS0VFBSkpKZKtgkaj4eDBg2g0Gpqbm9m4caPULUypVPaQjrW1tVFfX/9E70dG5udIa2srmZmZCILAV199xeHDh7l69Srl5eUcPnxYWt0/qtQyKSmJDRs2UF5eTm5uLt7e3s+s5+1zZ4/8XXQrbr79WEREBNbW1jg4OLBlyxbCwsIYMWKEdGxJSQlffPEFgYGB2Nvbc/r0aSwtLampqQHg5Zdfvk+V880331BVVcWMGTNwcnJ64r6y586d4+DBg/z5z3/G3Nyct99+my1btpCbm/vQEu22tjaSkpIQBIHKysoe7Q49PDwIDAzk4MGDuLu7Y2try/Xr1+nfvz9Dhgzhm2++wcfHhzt37kifk6OjI8OGDUOhUJCQkMC8efO+tzBNRubnTkJCAidOnJDEHJ2dnfTr14+FCxdSUFAgNT56FNLS0ti/f79kpdLU1MTy5csfmB5+Ah569XihAv6jsG3bNvLz87G2tmbEiBEEBASgUCg4dOgQt2/fRqFQ4OjoyIoVK9i5c6ckz/Lz82PixImSGVL3lwTAzMyM2bNn96pvTU5ODp6envz617/mL3/5C52dnRQUFKDVah8oCRVFkYsXL6JWq9FoNNy4cYMPP/yQtLQ0Tp06JTlxKpVKPvzwQ86fP09cXBxarVbaOO7GxMSExsZGRo0aJSmgZGSeV7Zv3051dTWNjY0sXryYxsZG+vfv/0h9Ku4lJyeHXbt2YW9vT79+/bhw4QIGBgZ88MEHvZ2vlwP+o9LZ2UlKSgrXr1+nrKwMZ2dnXn31VQRB4MaNGyQkJDB9+nTc3NzIy8tj+/btQFegVCqVjB8/Hj8/P4yNjamtraWyspLIyEhqa2t566237qugfRLmzJnDlStXyMzMZPjw4aSkpKBQKEhLS/vOeoHi4mK2bNnC2LFj0Wg0KJVKLly4IFXcurq6MnPmTNavX3+fNEwQBOkxXV1d3nvvvZ9Uz04Zmd6gtLSU06dPo9VqKS4uxsXFhaKiIn7zm988cuOkkpISkpOTGTt2LOXl5ezevRtzc3OWL1+Onp4e27Ztw9HRkfDw8N6e/ovTAOVJ0dHRITAwkFWrVjFr1iwKCwvZu3ev1HIwKCgItVpNTU0NTk5OqFQqTE1N0Wg0mJqaEhERwT/+8Q9iY2OxtLTE29ublStXolKpJBfM3uLNN9+koqKCadOmkZKSwh/+8Ae0Wi0HDx78ztc5ODhgZmbGhQsXuHz5MhcuXEAQBGbMmAF0FZyVl5fj6+srvaY7vdUd7AcNGkRHRweHDh26r2BNRubnTEdHBwcOHKCmpkaqu6mrq8PR0fGRg70oihw7dowbN26wadMmduzYgYmJCUuXLsXAwACFQsFrr732NIL9dyIH/IcgCAKBgYGMHz9eUqjY2dkRFRXFN998IznlWVtbS9bL1dXVzJ49Gy8vL86fP09VVRXQ5VUTFBTE7du3v7Nw64cyadIk3NzciImJYcaMGfzud78jJCSEw4cPf+97mzBhAiEhIaxdu5Zp06YxZcoUPD09USqVkl++r68vbm5umJiYEBwcLHXlAaisrGTcuHFS85b8/Gfidi0j06s0NzcTHx/fo7nQmTNnqKmpYezYsWi1WgRBoKGh4ZH8vVJSUti3b5+0qdu95+Xn58cbb7zx1BqbPCpywP8eRo4cycqVK1m9ejWvvvoqq1evJiwsjObmZkpKSqQvSnc13enTp/H29kZXV5eTJ09K3hjdVqj79++XHC6fFIVCwdtvv42uri4fffQR0JXmiYuLo7Cwy8+uoaHhgZ2y/P39mTJlChYWFgwePJghQ4agVCpxcnLCwMCA6upqDh8+TF5eHm1tbVhZWTF16lT09PRQKBQUFRVx5coV6dynTp2ira2Na9euPbADmIzMT5HLly9z8uRJvvrqK2pra8nPzycxMRE7OzsiIyPR09NjzJgxAPfp75uamnpU1dfX13Ps2DHS0tKIiorCxsaGCRMm8N577zF//nxJZ/9jIufwH4PW1lb++te/MnDgQKki18zMjPr6emxsbKisrJRUPEZGRgwYMIBJkyaRnJzMhQsXqK+vZ+XKlb1SyKTVaqmoqJDcQO/evYu3tzdjxoyhpqaGO3fu4O7uzqFDhx7JyrW7ObuDgwMlJSXo6OjQ2dmJIAh4e3uTnp4uPWZtbc3kyZM5ceIEdXV12NvbU1paytChQ5k8efITvzcZmaeJKIqsW7cOPT09qRudvr4+9fX1KJVKfHx8CA8Px8jIiPLycjo6OtBqtbi5uUmd6LKzs9HV1WX69OkkJCRQUlLCkiVLSEpKYtCgQT/I9bezs5M7d+5gYGDwpI6acg6/NzEwMJA0+wDDhg2TNOrdue5uyWZzczPXrl1j9+7d+Pv789ZbbwFIBU1PikKh6GH97OXlRUhICPHx8fTp04ff/va3tLW1ERoa+r25fegydHN1daWkpAQLCwvefvttVCoVKpWK9PR0nJyc6OzspE+fPjQ0NGBiYsKIESOAro0uY2NjacNbRuanTHFxMQ0NDYwYMYJVq1ZhYWFBXV0doigyZ84c5s2bh7GxsSTH3LlzJ7t27aKuro6YmBiys7MZO3YshoaGHDp0iPz8fCZPnoyrqyuzZs16aLDXarX3/X+0trayY8cOjh07xt69ezlw4MBTec/yCv8xuXz5MufOncPKyorVq1ezceNG6uvr0Wg0uLq6olKpyMnJwdDQkObmZgBJeqXVaqVGKE8DjUaDKIpSBXBFRQWzZ8/m2rVrrF27lpkzZzJu3LiHFns0Nzezf/9+QkND8fHx4fDhw6Snp+Pj48O0adPYvHkzLS0tUvetblQqFRqNBkEQcHFx6eFbJCPzUyMyMpLr16/z4Ycfoq+vj1qt5tChQ2RlZfHhhx9KG7QdHR18+eWXNDU10dnZiZmZGVVVVQwYMIA5c+bQ0tJCWVkZ9vb2j6RYO3fuHJcvX2bs2LFSumj79u0UFhYya9YsLC0tUavVT6LNl1f4vU231t3HxwelUsmMGTOkYGdpaUleXh6iKNLc3IyFhQVKpRKtVivl9JubmyktLf2uIR4bpVLZw+7B1taWs2fPsmTJEtavX09YWBiLFi2ipaXlga83MjJi+fLlUlcef39/Ojo68PPzo7KyksDAQFpbW7G0tJQat7i5uaFWqwkKCkKr1ZKXl0dCQsJTcfyTkXlURFEkIyNDWnQ1NjZy4sQJ/vGPf3Djxg08PDzQ19enrq6OpqYm8vPz8fLykoJ9e3s733zzDZWVlcyZM4cxY8ZQVVWFm5sbM2fORBAEjIyM8PDweKRgX1dXx5UrVzA0NOTChQuSVUpeXh4TJkxgwIABODo69nYhloS8wn9MRFHkzp079OvXT6o2PXnypORo6evry7Rp07h58yZnz55lzZo1tLW1UVlZKdkx6OvrS0qgR5V7PSmNjY1s3LiR//iP/yAgIIBdu3bh5+f3na/RaDSSv35NTQ19+vRhwYIFWFpaotVq+eSTTzAxMUGhUEg5/G7nze7OXs+qdFxG5l66a2VsbW0ZNWqU1BzI19cXXV1dBg8ejLGxMRs3bpSKC1966SV8fX1pampi9+7dlJWVMWfOHPz9/dFqtaSmpuLp6flYm7AHDhwgIyODd955h8jISNLS0rC1taW+vp5f/OIXT1yR/y/kwqtngVarpaGhASMjIymANzc38/HHHxMYGIirqyuxsbGUl5f3eJ1KpWLYsGGMGTPmqZkmfZvTp0/z6quv0tTUxN///ndWr179nUH5+PHjJCYmYmVlJTVp0Gg0aLVa8vPzyc3NxcDAAEEQaGtrQ6lUoqurS3NzM+7u7tTW1jJlypTvLAiTkeltvvnmG4qKiujs7ESj0WBnZ8eCBQskVZ0oiuzZs4ecnBxGjBhBc3MzEydOJDMzk6ioKFpaWpg/f36vfG/r6+tZt24dI0aMYMKECbS3t7N582ZqamoYOXKk1IypF5AD/o9Jty0DdHXZam9vl1QB96Knp8eyZcuwt7e/zx41OTmZ7OxspkyZ0mv+NWVlZaxYsYKIiAhmzJjBN998g4mJCc3Nzfz+97/n5ZdflhwAGxoauH37NkOHDmXnzp2PpbtXqVSEhYU9tW4+MjL3UlZWxueff8748eOxs7MjJyeH8ePHo1KpyM/PJycnh8LCQvLz8xkzZgzOzs5cvXqVoqIi2tvbsbS0ZN68eQ/1qvqhXLp0ifPnz7N27VosLCykOcbExDBlypRH9uN5BOSA/2NSVVXFhQsXGDBgAF5eXpSVlbF58+YHHqtQKPD19SUlJQUPDw8WLVpEZmamZLhkZWXFq6++KvnYPymiKPLPf/6TX/3qV/Tv35/333+fzZs3c+3aNQYNGkR8fLx04eno6ODy5cs4ODiQnZ1NcHAwJiYm1NbWkp2dTUpKClVVVQwZMoTS0lKKiooeOOZbb731vc2fZWQeh+66E0tLS0kj//7770uLpPb2dvbv3092djYKhULaU1MqlWg0GszNzfHw8MDT0xNPT88n9rgRRZGYmBisra2JiorC1NSU5cuXP+nb/D7kgP9T49q1a1Lq49y5cw89TkdHB41GQ58+fRgzZgx79+4lNDSUiRMn9up8IiMjWbRoEbW1tejq6vLKK6/w5ZdfsmfPHhYuXMjXX3/Nu+++S319PXPmzOHQoUP3nUMURQ4cOEBqairjx4+nrq6OpKQk6Z+q24fHwsKCNWvW0NzczKFDhxg2bJi0QSwj8zhotVppE1QQBEJDQ4mJiWHChAmMGDECURS5e/cuZ8+epaqqivHjx3PlyhWMjIyYM2cOCQkJmJubM2zYsMduWvQguhU53cyePfuR6mGeEDng/5TZs2cPJSUlPdI85ubmkg2DsbExvr6+ZGZmYmhoiI6Ozn2rhG4N/JOUbnd2dpKfn4+hoSF2dnYMGjRIsnj+4osvGDlyJFZWVpw8eZLS0tIH9upUq9V888035OXlAV29ASoqKmhubkZXV5fOzk5EUUShUCCKoiQfXbt2LTdu3ECj0eDp6Ym7u/tjvw+ZF48zZ85w7do1TE1NaWpqQqvVYmdnxxtvvIFCoeDw4cPcvn0bc3Nzpk2bxt27d4mPj+fNN998aneb3Y65gYGBWFhYkJ+fz8KFC793Y7axsRGlUvkkpoRywP850L0aEASBefPmUV9fT1RUlKRvF0URLy8vcnNzWbt2rSSJbG5uZt26dXh7ezN//vxem8+NGzd4++23iY+PZ/r06ezfv5+0tDSCgoLYtGmTVETWTXt7Ozt37uSVV16hubmZ27dvSw3RzczMqKurQ0dHB7VafZ9cs7tpfPet9erVq3vVWVTm+aS5uVlSwgUHB5OUlIRGo8HGxoZ58+ahp6fH5cuXSUxMZMyYMYwcOZK8vDx27drF4MGDmTp16lOZ15UrV4iKiqJfv34sWrTokcUYarWabdu2oVarefPNNx9X3Sbr8H8OjBo1Cn19fZRKJQcPHkRPTw8vLy/UajUKhQIdHR06Ojro7Oxk3bp1NDU1AUg+9xkZGWg0ml6bT0hICHFxcTQ3N3P8+HFJRtq/f3++/vrr+47//PPPef311zl06BAWFhaMHj2a5cuXs3jxYqn1oqGhoRTs/fz8CAoKArq+6NbW1kyaNAmlUtmjWYuMDHRVxubk5Ejf8cLCQj7++GPOnj2Li4sLLi4uUvqzpqaGffv28cknn5CYmMiwYcMYOXIkX3/9tSROGDdu3FOZZ1VVFVFRUfj5+f2gYC+KIsePH6e4uJixY8c+FSmzHPB/Qujo6DB16lRUKhWiKHLixAmsra2lVa9Go5GKtTQaDf/4xz/48ssviYuLA7qCZkFBAUeOHJFW1r3BvbeWgiCwdOlSyYcfkArK1q9fD3TdXnfj4uIipWi6ZZsKhQJDQ0NKSkoICQmRjq2qqiIuLg5fX1+Sk5Ol9I+MTF1dHdu3b+frr7/m448/pqSkhKioKAwMDLC3t6eyspL4+HiMjY1ZvHgxNjY2ktfTmjVrmDRpEnfv3qWgoIDx48fzzjvvPLHaraOjg6NHj5KcnExraysFBQV0dnYSFxeHQqFgypQpP0hmnZyczK1btxg7duxT29OSUzo/QdRqNadOneLmzZsAUmOS76Jv377k5OTQv39/UlJSEAThqeUnS0tLcXFxYe3atYwZM4bFixcze/Zsdu3ahY2NDSqViuLi4vtWKKdPnyYxMRFdXV10dHRoaGiQ7lruxdramqqqKvr06UNlZSWrV69+4H6BzPNPd63H/v37ycvLY9q0aZw/f57Gxka0Wi0TJ04kOjpaWhgEBwczffr0B55r+/bt1NbWsnbt2l7pMNUts7wXZ2dnKioq8PLyYu7cufe9pttbKysrCwsLC/r160dAQABtbW1s2LABW1tbli9f/qSr+6ebwxcEYTLwCaAEtoii+L/fel4P2AEEA9XAQlEU877rnC9ywIeuVfOePXvIysrC2dkZDw8PEhMTH9pI3MXFhYKCAul3pVKJi4sLr7zyitSE3cHBodduExcuXEhkZCRmZmZUVFTQ2tqKvb09v//973nzzTc5fvw4O3bsQEdHhwULFjB79my0Wi0ajYa0tDQOHz4sOXIaGBjQ1tYmqXhEUZQcOaHLetrHx4f09HReeeUVTE1NyczMlArcum/jv/3empubMTQ0lKt8f6ZkZ2dz+PBhyRYhKCiIkJAQ1Go1W7ZsAWDKlCmcPn2aCRMmkJCQwPz583vo5rVaLREREejq6hIbG0tYWBgjR4587Dm1tbURHR1N3759OXbsGK6urgQEBFBZWYmenh5RUVGIoshrr72Gs7Oz9DpRFElOTiYiIoL29nZcXFxoaGigrq5OSuO2tbUxefJkBg8e/Njz+xdPL+ALgqAE7gITgSIgDlgsimLqPcesAQJEUXxLEIRFwBxRFBd+13lf9IAPXX7b69evx8nJiSVLllBbW8uGDRswMzOjtrZWOq67GfK9dG+ChoWFkZOTQ25uLnPmzCEgIKBX5nbx4kXGjh0LdG02l5WV0adPH7y9vXF0dESlUqGnpye1eszMzJTcAzUaDZ988gmNjY1YW1uzePFiIiIiyMzM7KGNhp4tFQHCwsIwNze/z/kzJCSEyZMnS8E9NTWVAwcOMHHiRIYNG9Yr71nm2aDVajl79ixXrlzBxsYGf39/8vLyyM3NxcbGhvHjx7N3714AqT/Dw/rC5uTkSPtNSqWSX/ziF09U4BQREcH169el379dU5Kenk5xcTHjx4/vsdCIi4vj1KlTuLq6Mn36dKytrRFFkdzcXFJSUujo6KC0tJR3332XEydOSHtej8lDA35vCE5DgCxRFHMABEHYA8wCUu85Zhbw+3/9fABYLwiCIP5U80k/EYyNjRk7dixnzpwhKysLT09P/t//+3+IokhOTg779u1DoVDQ1NSEQqFAX19fSv2o1WpMTEw4e/YsCoUCY2NjLl26hL+/f6/czo4ePZqQkBC8vLzu2/wKCAggPT2dEydO0LdvXzw9PfnTn/4kFZsplUomTZrE7du3mTNnDvr6+pLs9N5gb2BgIDlyenh40NLSwp07d9DX18fc3Jzw8HDUajV5eXncuHEDMzMzhg8fTn5+PocOHUIURa5fv87QoUN7u0m0zFOio6ODXbt2SZXc06ZNo7y8nNzcXPr06UNZWRnnzp1DT08Pc3NzysvLGTBgwEP/vunp6ahUKl5//XVEUXysYJ+SksL58+fx9fUlLi6OgQMHYmNjg1KpvC9l6uPjc1/+Xa1Wc/nyZVxdXVm2bJl0IRAEgb59+9K3b19EUWTo0KEAfPrpp08a8B9Kb/wXOAKF9/xe9K/HHniMKIpqoB6Qk7KPwJAhQ9DT05O6ZOnq6qKnp4ePjw9eXl54e3sDsGDBAubOndtjI6pb16/VamltbaW6upqTJ08+UMmj1Wq5devWQ1NG30YQBK5du8aOHTvue27Xrl3ExsYyduxYXFxcWLVqFVu3bu3R6cvf35/Fixejr68PIK3+FQoFYWFhKBSKHvbL2dnZlJaWUl5eTn5+Pu3t7VhYWODv78+0adPw8vKS1EoXLlzA2NiYGTNmUF9fL20uy/x4xMTEcPDgwfs24evr60lJSZFy9QcOHCA/P1/a7Dx37hwXLlzA3d2d1157DX19fSorK/H09CQ4OBiAfv36PXBMURRJT0+nX79+2NnZ9egb8V0kJydL35mYmBgOHDhAW1sbMTExqFQqqZjrUS1Cbt68SWNjI6NHj+6x6u9OX4qiyPnz54mLi8PPz09a4D0Neq+krBcQBGEVsAr4QZ1inme6c/Hf9q4RBIHFixfT2dnJiBEjcHTsusb++te/JjIykqtXrwJdG77h4eFcv36d0tJSEhMTSUtLY/z48RgZGWFsbIyOjg4xMTGkpKSgp6fH1KlTGTBgwPfmvh/2fP/+/Xv8/p//+Z/s2rWLKVOmcPnyZWmu7e3t0mrGx8cHNzc3vL29CQ0NpV+/fmzbtg2tVivl8u+ltbWV8+fPs2jRIgRBYMiQIdy9e5fbt2+Tn5/PqFGjCAwM5OLFi1y7dq1XyuRlHo/uO62mpiZ8fX0ld1ZRFDl06BAFBQWYmZnR2tpKR0eH1IgkODhYkudOnDgRHR0dBg0axNWrV/Hy8sLX1xfgoW6vxcXFNDY2/iDFS1lZGUePHkUQBIKCgoiPj8ff359Zs2aRl5eHSqWS6l++j5qaGiIjI8nNzcXJyalHMWFLSws7duzAzMyM6Ohozp07h52dHfv27SMwMJBNmzbx97///ZHn/aj0Rg5/GPB7URTD//X7fwCIoviXe445869jrgqCoALKAJvvSunIOfx/09128Fe/+tUjfdk0Gg2fffaZ1ET9URk1ahS5ubkUFRVhZ2fH3Llze634KS4ujrCwMNzc3IiPj6exsZE5c+Zw+fJlnJyciI+Pv+/2uKKigpMnT1JQUHBfLr871z99+nSCg4O5desWx48fR6VS0dbWJuVWr1+/TkREBJ6enlIhjsyzpbCwkK+++gqFQoGpqSlhYWHU19dTXFxMWloawcHB1NbWUlRUhFarRa1WExgYyNSpU/n8889xc3OTlDdNTU3ExsY+1FJcq9WSlpbGzZs3KS8vp6WlhQ8++KDHna9Wq6Wtre2+SlZRFNmxYwfl5eWYmppSXl6Oh4cHixcvfiwX26NHj3Lnzh38/Pzw8fGhpqaGnJwcysvLSUlJwcXFhVu3bnHkyBEsLCxYsmQJ1tbWnD59Gh0dHS5dutTrhVe9scKPAzwFQXAHioFFwMvfOuYYsAy4CswHzsn5+0enuxlCfn7+favnB6FUKnn11VfZtWsX5eXlGBgYIIoiISEhXL58uUeeHMDOzo7hw4dTVFSEpaUllpaWZGVlceLECVasWEFtbS0mJiZP5Nk/ZMgQdu/ezfTp0/nv//5vzpw5w61bt/jv//5v/ud//oc5c+YQHR1NdHQ0f/vb3xg/fjyvvfYaK1asoKqqCj09PbZv3051dTXw77uLU6dOYWpqyuHDhwEk46zuC9XQoUNRKpWcOnWK8+fPy712nxHdqpSioiKpybcoitTV1fXYcO9eSbe2trJz507mzJmDq6srRkZGqFQqVq9e3ePOzNjYmPDw8IeOe/r0aeLj47GwsMDV1VWq/7iXmJgYYmNjeeedd3pYkWRlZZGXl8fUqVPx8fEhKSmJkJCQRw72HR0dJCUl0dHRwYgRI8jKyqJfv3784Q9/IDk5+b7jw8PDuXjxIu7u7ixZsgSVSoVCoWD8+PGYmJggimKvK8yeOOCLoqgWBOEd4AxdssyvRFFMEQThj0C8KIrHgC+BrwVByAJq6LooyDwi9vb26OjokJeX90gBH8DExIQJEyawc+dOWlpaCA8PJzQ0FBMTE06cOIG+vr4khSwvL+fIkSMolUr09fVpamqSbqdPnjxJYmIivr6+LFiw4DvHVKvV1NXVYW1t/cDnp02bxty5c/nTn/6EIAgcPnyYWbNmSeeeMGECN2/exMTEhJiYGP7xj3/wySefsGzZMhQKBXPnzuWLL74AkPYhtFotu3bt6jHOt1fxgwcPJj8/n+TkZMLCwsjLyyMnJwdBEBg3bhw6Ojo0NTVRU1ODnZ2dfBfwBHR0dKBWqzl79iyJiYmSvNbU1JSGhgYGDRpEXl4etbW10gp727ZtGBsbY2hoiJ+fXw/zsh+yslar1dy6dQt/f3/mzJnzwBSeKIrcvHmTjo4OYmNjeywAkpKSMDQ0JCgoCKVSyahRox557Pb2djZu3EhtbS0dHR0YGBjQ1NREXFwcycnJzJw5kzfeeIPq6mrS0tK4ffs2p06dQqlUMnXqVMzNzZk9ezbu7u6cOnWKlpaWp5KC7JUcviiKp4BT33rsd/f83AZ8d7SQeSjdefz09HQMDQ0JDg7G1NSUrKws+vTp89A0j4uLi/SlGTBgANBVmNKvXz9MTU35+uuvKSwsRK1WA/Dmm29iYWHBF198wd27dzE1NSUhIQF9fX1SU1PJzMwkKSmJkpISVCoVK1askKwSuouqNBoNL7/8stQC8tt88sknJCcn89577zFr1iwA5s2bx+bNm3njjTfw9PTkypUrNDQ0sHz5cl577TX++c9/MnToUHJzc8nIyGDAgAEMGTIE4IGVuKWlpURHRzNs2DD09fXRarVYWFjQ1tbGkSNHSE1NlWSr3YEnMTER6Cr6ev311+Wg/y+0Wi03btygoKCAsLCwHgVwtbW13Lhxg9GjR2NgYEBRURHffPMNHR0daLVa+vXrhyiKZGdnM3LkSDIyMqRiwkWLFuHt7U19fT1nz57l9u3bjB079omcKnNycujo6CAgIOC+YNmdKiotLaWurg4zMzMSEhKwtramubmZkJAQ7t69y6BBgx4rfZOZmUlDQwM5OTns3r2bM2fOMHbsWE6cOIGpqSmBgYGSc6ytrS2DBw+msbERV1dXxowZQ1hYGJaWlgBMnz79qVWYy5W2PxNSUlKIjIyksbERS0tLgoODiYyMxNfXl5deeumhr9u/fz+6urpScL2XjIwM9uzZI632DQwMCAsLo6OjQyogAXB0dKSmpobW1laUSiXe3t6kpqYyadIkhg0bxo0bNzh9+jQBAQHk5uZibW3Nq6+++tA5PexW9dKlS3h7e0u5fI1Gw65du/jzn/9MVVUV7u7uWFhYEBUVxVtvvcUHH3zAzp07ga66A1tbW0pKSnrk+7tvkzs6OqTHnZycMDIy6qEaGjp0KNbW1pw6dQo3NzcMDAxwdHRk+PDh0jHfbkrzPKHRaKioqEBHR0e6Q1Or1Xz99dcUFBSgVCoRBIHx48dLMtedO3eSnZ2Nk5MT1tbWJCUlAfSopbCwsKB///6MGTNGCob+/v7Mmzevx/jNzc0YGBg80ed79OhR0tLS+PDDD+8L2ufPn+fKlStYW1tTU1PDa6+9xueffy59T7oln98umHoYCQkJVFVVSemlAwcOkJKSwkcffYSlpaX0Wba2tkrFXvd+L8eNG4eenh729vZPQ6DyVHP4Ms+A/v37079/f/Lz89mxYweRkZHo6OiQkZFBU1PTQ1f535WG8fLyYsGCBTg6OnLs2DFycnI4ceIE0JUS6pZ1VlZWoqOjg7m5OaNGjcLDw4P6+nouXbpEW1sbsbGx9OvXj9mzZxMbG8vZs2cpLy+XLBbMzMx6NGV+WF5y9OjRPX5XKpW88sorvPLKKz0e/81vfsNHH32Ejo4O48aN49atW6jVakpKSnB2dpYar5ibm+Po6EhDQwN9+/bl+vXrtLW1oa+vT0ZGhtSucdiwYUyaNAlAutjp6OiQmpqKnZ0dHh4elJaW8tVXX+Hv78+kSZN6revYT4HGxkY2b95MU1MT+vr6/OpXv0KlUnHt2jUKCgqYPn06Xl5enDhxgsjISOLi4lCr1dL3o6ioiKKiIpRKpZSWyMjIwN7evkcFtKenJ7NmzXqgauZJuz1pNBrS09Px9vZ+4Ao9NTUVrVZLWVkZAwcOxM7OjldffRWVSkVSUhIJCQmYmZk9knRTq9USGRlJe3s79fX1TJ8+nYyMDK5du0ZrayuzZ88GYPfu3bS3t+Pv74+ZmRn19fUIgoC9vT0jR478URYP8gr/Z0hKSgopKSmMGDGCLVu2MH78eBwdHbGxsXlsP/zOzk6OHTtGeXk5lZWVAAQGBtLS0kJmZiaiKOLs7ExxcTFKpRIDAwMaGhoAMDU1ZfDgwZiamuLp6cnHH38MIKWKdHV1ee+993qoItrb28nIyKC9vR1fX1/pgiWKImq1+js3iEVR5MMPP+Tvf/8706ZNY/r06YSHh7N161bS09NxcXHBw8ODiooKqqqquHv3Lm5ubtJeiFqtxtXVlSVLlvDZZ5+h1WpZu3YtVVVV6OvrI4oiBgYGfPHFF7S0tPDmm29y4sQJcnNzUavVksa/srISjUYjrd5+rly+fJlz584xYsQIYmNjmT9/Pk5OTqxfvx49PT2mTZuGr68voihy+/Ztbt68SWlpKaIoYmpqSl1dHWq1mqlTp0qptmdNdnY2O3fuZOHChTg5ObFr1y5GjRqFr68vtbW1/POf/2TixImYmJjg7u7eY4GkVqs5ePAgRkZGJCcns2bNGqkF4b10CwZu3brFpUuXSEhI4Pjx44SGhjJy5Eg2btyIm5sbGzZs4OLFi2g0GpycnCgrKyM8PJxz586xcOFC7O3tn/aCQV7hP090r/ahS8Fz/vx5RFHEx8eHhQu/07Hioejo6Ei32Z2dnXz55Zfk5eVJLRahS14HXd423ReF7uO7u3YFBgYybtw4srOzaWpqYsiQIZw8eZLr169LFbndjaO7m6TEx8ezcuVK8vPzuXjxIuXl5UyfPv2hnYEEQeCvf/0rdnZ2/OlPf+LkyZPs2rWLvLw89u/fT1hYGCYmJnR2drJnzx5Jnvree+9hbW2Nk5MTPj4+rFu3TqpMjoyMJDExEVNTU9566y2USiXz5s3jyy+/ZOvWrdTW1jJu3Dg8PT05ePBgj41iQRAYMWKE9PPTorva9LuCRUpKCiYmJg9ME7S0tBAXF4epqSn9+vWTlCBJSUm4uroyfvx4bt26xYULFxAEAbVajVqt5tixYzg5OZGfn09paSlVVVVotVoWLFiAubk5mzdvxtraWiqEelbU19dz+PBhZs6cSWpqKrq6unh4eBAbG0tpaSmHDx/G2tpa+p55e3vfZ8IniiLNzc0sXLiQ7du3o1arSUpKYty4cVy/fp2PP/4YR0dHvL29KS0tldIyJSUlREREoK+vz7Vr10hLS6Ozs5NRo0ZJdwv19fVUVVXh4uJCSEgIwcHBvdpN63GQV/g/c7KysoiOjkZPT4+SkhI+/PDD7+2o8yh0r5gMDQ1pa2u7r/cn/Du46enpSXn5trY2hg4dSlJSEu3t7QQFBdHS0kJubi4DBgxAFEVMTEy4cOEC4eHhWFhYsHfvXvT19WltbcXMzAwTExOKiooYOnQoEydOvO8WvbW1lYSEBIKCgtBoNEyYMIG8vDw0Gg3V1dUYGRnxy1/+ktTUVA4ePMj8+fNJSkqiuLiYv/3tb3z44YcMGTKEcePGMWbMGC5evNjj/N0r1eTkZI4cOYIgCOjp6fHee++hr69PXl4eERERuLq60tTURGpqKjo6OhgYGPDSSy9JhWW9SbeW3dbWlldfffWBKZD6+no++eQTACZPnsyQIUOkv1FHRwc7duyguLgY6Po7hoSEYGtry9GjR5k1axYBAQFs2rRJukAKgkB4eDhRUVEolUo6OjpQqVTY29szffp0SfpaUVGBvr5+r/VZflS6m4wMGDCA7Oxs3N3dmTNnDuvWrcPc3Jza2lp0dHQwNDSktbWVd999974L8u9+9zv+7//+j5MnTxITEwN0paju3r3LpUuXJHsPPz8/KisraW1txcnJiczMTExNTVm5ciW7d++mrKyMAwcOkJmZSUtLC3PmzOHEiRN0dnZKlbnPELnj1fNOfn4+27ZtY/78+Y8s3fw+ujflZs6cSUtLC+fPn0dPT0+S3gHY2tpSUVEh/VOpVCo6OzsxMjKiubkZpVLJsmXL2Lp1q+Tzr1ar6dOnD6tWrUIQBOLi4oiPj2fo0KEMHDgQQRCIjIzk+vXruLm5sWjRInR1dampqcHMzIxdu3aRm5uLlZUVixcvJjs7m2HDhqHVapk0aRKRkZEMGTKE+Ph4goOD+eMf/0hERAT//Oc/JXWOkZERv/jFL5gwYQIVFRWkpqZiY2ODkZERZWVlLFmyhD179tDc3IwgCEyePJmQkBBu3LhBRESEZOtsbm4u2Vt076f4+vpib2/P4MGDH5iaKigowMjIqMdq8/s013v37iU3NxeNRoOlpaUU9DUajeTemJ+fz5UrV3BzcyM3N5e+ffsybdo0zMzM2Lt3L1lZWSxYsABLS0tiYmK4c+cO0JVyW7JkCZcvX5ZK+rtfa2lpyY0bN7hy5Qrjx49/pArsZ4FareaTTz7pYRrYr18/KS2zePFijIyM2Lt3L42NjQwZMuS+7lZJSUkMHjxYSr0EBQVx+/Zt6bsVGhpKcHAwUVFRXL16FVdXVwwNDcnLy2P48OEMHDiQOXPm4OvrS2lpKf7+/ty5c4eMjAzmzp3LwYMHSUlJYc2aNdjY2DzLj0cO+M87Wq2Wf/zjH7i5ufVam8OmpiaKioqkTbbbt29Lzctfe+01UlNTuXbtGsbGxixZsoT8/HwiIiIAetgbDx8+HI1GQ2hoKGlpaY+kLoIuT5OjR4/i6uqKrq4ud+/elQL2sGHDSExMpL29HYVCwZUrV6irq2PixIl88sknNDQ04OjoyNWrV3F2dkYURcLCwjh//rxUY/DWW2/h4uKCl5cXmZmZNDc3M3jwYEltci9KpZJp06Zx/PhxPD09mTNnDsXFxezatQsvLy9eeuklWlpaOHXqFMXFxdTX12NmZsasWbNwcHBg//79GBkZMXDgQHbt2oWpqSlvv/02SqWS7Oxsdu3ahZ6eHgYGBiiVSgYOHEhISAg6OjpUV1ezfv16Ro0ahbu7O7t27cLS0pKpU6dy48YNUlNTUSqVqFQq+vbty/z584mPj+fcuXOIooiDgwN5eXk4Ojry+uuvA3DixIn7uorp6ekxduxY3NzcsLa2/tHTDw8iPj5eqkRtb2/v8T0TBIHS0lJ0dHRYt24dCoWC5uZmLl++zI0bN8jMzOSrr75CR0cHrVbL0KFDKSws5NNPP2XhwoWIoigVIfr7+2Nubk5jYyM6OjrU1tbyl7/8hdTUVKnIz8jIiLVr1z70jrqiooL09HRGjRr1rC+Scg7/eUehUODj48OtW7fo6OjolbSOsbFxD0WFj48Purq6ODg44OzsjJOTEyqVipiYGMrKyhgyZAjGxsYkJCSQm5sryT2vXLkCdOm2u1dk+fn5kszx7t273Llzh2HDhmFvby+N173aP3z4MAqFgpEjR1JXV4ednR0jR46U/HNqa2t57bXXaGlp4ezZs6xdu5aoqCjGjBnDvn378PT0xNvbm3379nH06FHy8/O5e/cu58+fZ/HixdJGZEREBI6OjqxZs0byYO82rjM1NeXYsWNYWloyatQo9u3bx4ABAxg0aBAJCQlEREQwfPhwmpubCQ8Pp729nRMnTvD1119jYWFBTU0NgiBw+/ZtFAoFtbW1JCYm4u/vz9GjRzE3N8fd3Z2Ojg4aGhqIjo4mKSmJFStWEBkZKaVgjI2Nefnll9m9ezfbtm0DYMyYMaSkpFBVVSVJJkNCQvD29ubAgQNSDru6ulqy5E1ISCAkJAQ7OztqamqwtLTE19f3J6U+6i6OcnJywtPTkzt37nDq1CnJcAzA0tKS0tJSNBoNo0ePZtGiRbS0tPDhhx9SWlrKjh07uHPnjpS28/Dw4Pe//z0nT54kPj6eTz/9lIaGBl566SVUKhXe3t5S+rKxsVG6cxo/fjwqlYqAgADs7e1pbGzEwsLiO//PbG1tH8maRBRFTp48iZGREePGjaOlpQWVStUr/8PfRl7hP0cUFBSwdevWp6qWKCkpwcTERFIDiaLIV199RW1tLR4eHty6dUvKe65cuZIdO3bQ2dlJv3797nMAXLlyJU1NTezfv1/6JwsMDGTw4ME98uCZmZkYGBhgZ2fHoUOHMDExeaTm0xkZGdy+fZvMzEw6Ojqws7OT9iOOHDlCTEwMo0ePpqysjIyMDCwsLKitrWXevHlStW/3nBUKBRMmTCA8PJysrCw+++yzHnJOQEpj6evro9FopKYW0BU8jI2NEQQBfX19ySBMq9XS3t6Ok5MTM2bMAODw4cOYm5uTkZGBnp6e1Bij2z63WxZoaGiIo6MjLi4uHDp0iJycHNauXYuhoSHl5eXY2dkRExPDuXPncHV1JT8/n9WrV3Ps2DFaWlpYvXr1E9llPE2Kioo4ePAgdXV1KJVKhg4dypUrVySV1b1x6/Tp09y6dQsrKyuamppobW1l3LhxXL16lc7OTmxtbfnFL35BfHw8u3btYsuWLXz00UeUlZXx3nvv3bf6njBhgrRAqKqqemBDk97k4sWLUkvSVatWERUVRXt7O6+//vpP0ktH5idC96r76tWrBAcHPxWd773dhAApv71lyxZu3bpFQEAA2dnZuLi44OTkxNKlS9m6dWuPYG9vb09paSmnTp2ivLwce3t7FixYwPXr17l69SpJSUnMnz8fT09Pmpqa6NevHxqNhgMHDkjFUn5+fri5ufWYS1NTE9u3b8fS0pJBgwbh4+ODt7e3pNE+ffo0zc3NLF++XLKQuHjxIiqVivDwcEJCQvjqq68kL30TExPGjBmDu7s7SUlJREZG0tnZSVlZGaIocuXKFWbOnImxsTE5OTnS3yAxMZHCwkK2bNkiebts3rwZZ2dn3n//faqqqqitrUVPT4/6+nrJTbKtrQ0dHR3KysooKysDujosdVsBR0VFMXDgQDIyMqQmHH5+fpw8eVJqiJOenk5HRweRkZEMGDCA1NRUfH19mTBhAp9++im3b9+muLiYsLCwn2ywv3PnDkeOHMHU1JTFixcTFRXFlStXpK5uo0aN4j//8z/R0dEhNDSUGzdu4O/vT3l5OR999BHp6el8/PHHmJiY8M477/C73/0OQ0NDTp06xcmTJ1mxYgXQVeHdHVCVSiWenp5MmjRJkmTOmTOHLVu2YGJigpOT02O/n+TkZCwsLO5TTt28eZPk5GTy8/Px8/MjJyeHHTt20NbWxsyZM59KGkhe4T9npKWlsW/fPsaNG4e3tze2trbPJH8YGxuLIAgMGzZMWoF135KePHmShIQEpkyZgqWlJUlJSaSkpCCKIvr6+ixevFj6Z9i4caMk+eyu2HR0dKSxsVHqgavRaLCysuKtt97qcVHrXind69vS3RQeumSJtbW1lJeXY2hoyI0bN7h48SJubm6MGTOG9PR0kpKSOHPmDH5+fqxcuVIyvdLT02Pnzp2kp6ej0WgYMWIElZWV3L17Vxrf2NiYV199lQMHDlBRUYGnpydDhw7l8uXLkr31ypUrcXZ2pr29nYaGBqysrCTHRAcHB2bPno2bmxstLS0MGzaM5ORkFAoFQ4YM4fz581haWkp3BqampnR0dODg4MCwYcOIiIjAxMSEmpoampqa0Gq1GBoasmbNGqqrq9m7d6+04f7OO+/8KH2C29vb0dXVlb6T3R74f/rTn3B2dmbhwoXk5+fj5OTEtGnTaGtrQ6FQkJubi5GREcePH6ezs5M///nPCILA7NmzOXz4MOvXr++hLoqPj8fW1hZnZ2cGDhxIZ2cnqampdHR0cPbsWcrKyli6dCmGhoZS8aGuru59+xYpKSno6uo+1Crk+2hubuZvf/ub1NS8u31hdwcsW1tbvLy8GD16NHFxcURFRREUFCTd7T0m8qbti4JWq+WLL76QVoiGhoaMHj1aSgf8GHS3arSzs8PJyYkrV66gp6dHe3s7+vr6CIJASEgIQUFB0mYbgK+vL9XV1VRUVKCrq4u1tbVUCwAwcuRIwsLCgK73vW7dOiwtLXnllVe4cOECMTExODk5sWjRIknGWFZWxueff463t7eU71UqlZJ3zuHDh6X0QH19Pa+88gqnT5+W9h/+/ve/09nZyfvvvy9tuKpUKhobGzl//jwajUZyS7x+/bqkZnrppZeIioqSHCC3bdtGQUEBY8eO5datW4iiSEdHB3p6etJm7r10F8YNGTIEV1dX6WL561//Wgqe58+f59KlS9JrHB0dmTx5Mubm5qxfvx7oCrh2dna89dZbT+NPLaXmHnR3WV1dLd1laDQa1q5dyx/+8AcuXbqEpaUlGo2G+vp6li1bRmhoKMXFxaxfvx59fX1WrFiBr68vqampbNy4ESMjI6qrq+no6MDW1pY1a9bg4eFBQUEBnZ2dGBgY0N7ejpeXF+np6UDXhWDgwIGkp6ejr6+Pv78/wcHBmJubP5XPArruVg4ePChZN0ycOBGFQsGZM2ekzf7uv7VWqyUzM5N+/fo9lp/PPcgpnRcFhULBypUrqayspKKigqSkJCIiIrCzs7svBfKsMDY2ZvLkyRw9epSCggICAwOZMGECH3/8Me7u7qSnp3Px4kWSkpIkNU1kZCR37tzBwMAAGxsbKisrKSwsZPjw4SQkJGBoaEhMTAxNTU0EBgZSUlJCY2OjpIsPCwvD3t6ew4cP89VXX/H6669jYGDAtWvXgK76hYaGBjZv3kxnZycDBw5k0qRJ0sawv78/p0+fZuvWrSxZsoSCggIuX77MkiVLaG5uxsTEBF1dXcmUDro26b7++msGDx7MxIkTmTZtGllZWVILO5VKxZ49e/jjH/+IIAg4ODhIudslS5agVqvZu3cvaWlpTJs2jeLiYoyMjGhoaCApKYnbt29TV1fHypUr0dXVpa2tjaqqKuLj4/Hy8qJ///5SwNfX16e4uJiCggISEhJob2+X5tndOKSsrAylUomFhQUqlUpqMn9vqqf7YtsdFNvb20lJSaG6upr29nZcXV2xsrLCwMBAqkBWKpW89dZbjBo1Cn19fS5evMjAgQOJiIhg/fr1VFdXIwgCR48exdDQkBkzZjB37lyys7PZtGkTR48excfHB4VCQV1dHTo6OnzyySc4ODhIZn+nT5/mm2++YePGjZKFcWNjo6TYaW1txcTEhIKCAuDfvZHb2tpoa2t7qMXDk1JSUkJubi7Dhw9HEARycnLQ09Nj5cqVHDlyhKioKKCrCGzevHk9ArtCoZAkvk8LOeA/h3QXx9jb2+Pr68vmzZslK2J3d/cfRUfdnXsuKSmRvGgCAgIk90RA8hrx8fGRzKeGDBnCZ599JvnmhIaG0tHRQffdX1JSkiSj7FYFpaSkMGDAAPz8/DAyMuLrr7/mwIEDUh9dZ2dnCgsL2bt3L83Nzfj4+BAXF0dLSwvNzc0UFBRIgQLgyJEjNDc34+vrK6WZXFxcWL58ubRSVygUuLm58ctf/hIDAwOsra2pqqrC09MTrVaLiYkJQUFB2Nvbk5qaipmZGb6+vmzatAk7Ozs2bNjAyZMnpZL9uXPn4ujoSH5+PlZWVly7dg2lUklhYSH5+fkYGhqSmZnJtWvXqK6uZujQoXzyySc4OztLzpZpaWlSgOnWiBsbGzNw4EBSU1PZv38/0LUv8/rrrxMREUFKSgqvv/46FhYWVFZW8tlnnyGKIo6Ojixbtox3332XLVu28NZbb+Hg4MCNGzek9zBp0iTOnDkDgI2NjVT9bGhoKJnsVVdXs3nzZurr67l8+TLu7u54enqip6eHs7MzM2fOZOvWrRw5cgStVouDgwO/+tWv2Lt3L3l5eQQEBDB69Gh8fX357W9/S15eHr6+vmg0Gmpqapg9ezZHjx5FFEW0Wq2kBFuzZg2nTp0iPT0dc3NzvLy8nuj73NnZiVqtvq+xyuHDh6mqqsLY2JiAgABycnJwd3dHpVIxZ84cjI2NsbS07FEU911eWL2NnNJ5ASgpKWHnzp20trZKqYwfg2/75FRUVLBp0yb69euHt7c3J0+elLoihYeH4+3tTXR0NFevXkWhUNC3b18CAgK4fv06RUVFDBkyhKSkJDo7O/Hx8aGxsZHi4mJUKhW//vWv0dHRQRRF4uPjOXXq3+7d7777Ljt27KC+vh53d3deffVVYmJiOHv2LNBlT2thYYGhoSGHDx+moqICHx8ftFotd+/elTYPX375ZRoaGiTDuQchCALu7u7Mnj2b0tJS9u7di1arZcCAAZiYmKBSqVAqlSgUCgYPHsyvf/1rPv30U+n1ffv2xczMjJs3bzJr1iyioqLo7OyUVrLdVc4dHR04OTnh4uJCVlYW1dXVfPLJJ4SEhFBZWUlYWBjvvPMO27ZtY+XKldImpI+PDykpKRgbG9Pa2opGo8HQ0JCXX36ZCxcucOfOHcLCwoiNjWXw4MHMnTuXjo4OBg8ezPz588nKymLLli0IgsCgQYNITEyU0mfNzc0YGxtLFht3797F09OTuLg4RFHk1KlTJCQkSN5F3VYOly9fJjo6Guiqeg4JCQG6Fg0NDQ3k5uYyYcIE3N3d2bJli6TY6X5fH330EZ2dnbz77rt8+umnBAQEMHPmTBobG9m5c6dUNPW4dHR0sHXrVhoaGli2bBmJiYmUlZXRt29fzp8/j7GxMWq1mnnz5vHNN998p2ru7t277N69mwULFjy0VeNjIOfwX3S6m3vHxsby6quv9uiv+WOSnZ2Nvb09hoaG0gbomTNnqKmpwd7enpqaGvr164e9vb0UBAwNDaVVdkVFhXTb39nZKa3eFy5ciI+PD8eOHSMzM5NJkyYRFxdHYWEh4eHhFBcXc+fOHV555RUp5XLlyhXMzMzw9/eX5ted8zc0NKSlpYUpU6YQFBTEF198QXNzMyqVCgMDAykXn5qaKr12yZIlODk5SY3a4d853W6vlXvplk5mZGSgq6tLU1MTCQkJFBcXY29vz5tvvsmVK1fIyMhgwoQJmJiYSNW2CQkJ3Lp1i4qKCqytrRFFkfLycoYNG4alpSWBgYH85S9/kVJENjY2LF++nKqqKjIzMxk7dqxkgdx9AYmOjiYuLo7AwEBmzJjBxYsXuXjxIv369aO4uJj333+fDRs2YGFhQUlJCZ2dnVLF6rFjxwgMDGT27NmcP39e0sEfOHCghzVyfn4+eXl5UmeyiIgIkpOTuXHjBnfu3OGNN95Ao9FIF6Ju7yMnJycaGxupr68nPDycK1euYGBgwKJFi/jnP/8JdHk+1dbW8s477zzQDO1REUWRyspKqVp279693L17F319fdrb29FqtVJBYJ8+fZg3bx6ff/65tH/z7Q1yURSpr6/H3NycgwcPcufOHfT09Fi1apXkif+EyAFfpivo//Of/8Tc3JwVK1b8JErkH4RWqyU5OZlLly5RV1fHG2+8gb29PeXl5QiCgKWlJbGxsVIQ6V5FAowfP56YmBg8PT3p378/+/btA7qsebOysjAyMupRju/h4cHEiRMxNTV9aNHRl19+SUVFBTNnzpRsKyoqKti8eTMajYalS5fi4eEBQGJiIleuXKG6uprQ0FDJL/1er6G//vWvkvlYt4oqLy+PEydOIAgC77zzDp2dnaSlpaHRaBg4cCDm5uao1Wq2b99OWVnZfRWmDg4OFBcXS8VycXFx7Ny5k/z8fCnwWFhY8Oabb1JcXMzu3bvR1dWVAqiHhweTJk2iT58+BAcH8+GHH5Kenk5oaCjx8fHSWD4+PnzxxReMGjVKSm+dOHGC/fv3s337dn75y1/Sv39/rl+/zsSJE5k1axaVlZVMnz6dhoYG0tPTH1rBm5uby/79+7GxsZGURkqlUtrXiYqKQldXFz8/PymN170B3d3boTvwKpVKLC0tGTt27BOtnLub5nTbJQiCwMGDBwkPD8fV1ZWDBw8SEhJCv379iIqKYvjw4Tg7O1NbWysZqo0ePbrH/1pSUhJHjx7l1VdfZc+ePbi4uFBUVISZmRmvvfZabxRcyQFfpotuOdi9QeqnSrdq40GrnsbGRtatWwd0deratGnTA8/Rp08f7O3tuXnzJnp6erz77rtSKzu1Wk1ERIS0QluxYgV2dnaUlJTg5OQk/ZO2tLRI1Z1GRkbS46mpqZSVlTF+/PgeY3YbnRkYGPDhhx+i0WjYtm0brq6uTJw4kZiYGKmV3r1cvXoVURR7NF35Nm1tbdy6dYvs7Gz69u1LdXU1t27dQl9fn87Ozh6qo6CgIBISElCr1RQXF2Nubs6YMWO4evUq6enpHDp0iGHDhmFhYcGxY8fQarXY2dnxyiuvSH2Fp0yZgomJCTdv3sTQ0JAVK1YwYMAAfv/731NdXc3s2bMJCwsjKyuLDz/8kC+//BILCwsqKiqki1m3TLeyspKEhASGDBki+c7n5+dTXl6OpaUl+/bto7OzU7qYdRfwAVLjHV1d3R7WF4sXL5by8dnZ2Zw/fx5DQ0Pmzp2Lnp7eIy1q1Gr1Qy9C27dvp6CgAENDQ/T09FAqlWi1WtasWfOd5y4rK8PKyuqBtQ67du2SiglbW1t5+eWXEQSBXbt24e7ujpmZGbq6uk/Sf1kO+DJddJtO2dra3tdY5OdGdHQ0arWayZMnc/DgQXJzc5kyZQoajYajR49ibGws9Qvds2cPw4YNIyQkBI1Gw/nz58nNzWXatGnU1tZy5swZDA0NsbKyIjU1lTFjxjB27Fhp06+4uJgtW7bQt29fZsyYgbm5OZ2dnbS2tj7QJXLTpk1UVFQwfvx4CgsLJYtpfX19DAwM6Nu3L25ubvTv3/+J77S6vXi0Wi19+/ZlyZIlCIKAIAhcu3aNM2fO4O/vT0tLi1QgJggC/v7+3L59G+i6gJaUlHD8+HGamppwcXFh9erVWFhYSA6hq1atwsrKitLSUlxcXB4476SkJLKystDX12f48OEUFxdz5MgR+vfvT2VlJWVlZRgbGzNlyhROnTolWVgAUspGR0cHGxsbSkpK6NevH6GhoRw5ckS6OzMxMZGM+dauXftIn19NTQ2lpaX3GQt2VyK7ublJXkXddBsShoeHY2ZmJt0tzpkzh4CAAERRJDU1lX79+vVoiXnz5k2OHTtGQEAAc+bM6TFee3s7f/3rXzE1NZWK77o7dHV3jtPT08PX1/eBXeoeEVmWKdOFSqVi6NChnD17ljt37pCZmcnIkSOftZtfrzBhwgTp57lz5wL/tmzWaDQcO3aMPXv2oFQqmTt3Ln5+frS3t/PNN99Iev6amhr8/f1RKBTs27eP8vJy+vTpw8WLF0lPT6eyspJly5aRnJyMSqWiqKiI7du38/bbb7N//34pEH67cXtISAgnTpyQ+gRAl+yue9M6ISGBhIQELly4gJ2dHa6urgQGBiKKIteuXWPQoEGSTbSlpSXNzc0P9WXx8PBg/vz5JCYm3te829jYGIVCgb29PcHBwVIhmZubG/r6+lLAHzBgAAsXLiQoKIidO3cydOhQXFxcqK2tlbx4rl+/LjXECQkJkdJV3X0EdHV1OXr0KCYmJrS1tXH79m06OzuxsrIiJSUFQRAYO3YsV69elRRCVlZWvPTSS1K/5NbWVqZMmcLJkyfp168fixcvRqFQEB4ezsGDBxEEgSVLlkjWFY96sYyKiiI9PR0HBwcpn5+fn8+5c+ekFp5ff/0106ZNIzg4mPz8fLZv346+vj5BQUHo6OhgZ2dHZ2entMdTUFDAgQMHCAkJYcqUKUBXodbx48fR19fn1q1bDBs2jD59+nDz5k3i4uIkRdGMGTM4e/YsDg4OkjSz2//IxMTkqXXDklf4LyCtra18/PHHUl7W0dGRlStX/mRz+o9Lbm4uLS0tXL9+ncLCQgYPHkxNTQ25ubnMnj2b6OhoHB0dpaYx586dw9jYmODgYPbv309DQwMNDQ2Ym5tTVVWFj48PAwYMYOfOnQQEBHDr1i2gS3//+uuvS7fvWq2WLVu2UFpaCnQF+u52ekePHqWyshI9PT0p+HdbLJiZmWFtbU12djZWVlY4Ojpy69YtLCwsaGhokFbc7e3t9+03aLVaaa7dtLW1sX79ejo6Oujs7Oyxp9DNoUOHqKmpYfny5Xz66ac0NjZK3c1ee+01EhMTOX78eI/XdKuUugNgTU0N0GWz3N2ke86cOZw+fRqAsWPHkp6eTmZmJpWVlXh7e5OXl0d7ezuCIPDee+9RVlbGnj17pDH09fVZvXq1dPckiiKnT5/G0tKS0NDQR/r7x8bGUlhYyMyZM/nHP/6BRqNh+PDhTJw4kba2NjZt2oRKpWLVqlVA14ZyVlYWAwYMoKamhuLiYjw9PXn55ZeBLtWRVqulubkZOzs7qYJcqVTyzjvvUFlZyZ49e3B0dGTBggVs2rQJKysr/Pz8evSINjAw4IMPPpDuwp4C8gpf5t8YGBgwfvx4Sf0RFRVFYmJij45FpaWlWFlZPRXHvmdF9+25l5cXZ86cITExEa1Wy8yZMwkICKC4uFgqStLT0+uRi+++CNwr6Rw4cCBubm64urpy69YtDA0NmT59Ovv27ePw4cOEhYVx9OhRysrKpMYXZ8+exdnZmV27duHq6spbb71Fbm4uoiiSl5dHbGwsK1eupKSkhMjISMmHqKSkhOrqanR1dSWfnOPHj2NlZUVSUhJBQUHU1NRQVlZGSEgI2dnZFBYWMnfuXLy9vcnNzeXu3bu0tLTw+uuvk5SUxLVr17C3t8fT01Nq7l5dXU1dXR3R0dE0NDSwdOlSUlJSuHXrFvX19aSnp2NiYoKbm5t0N1BQUIAgCJSXl0ufl0KhkGS3JSUlxMbGsnTpUvLz8/nqq6+ALm2+n59fDyWTKIpERERId1zh4eGSDPbeVJkgCEydOpXa2lr279+Pr68v+vr6FBYWMmzYsB5KKOiSIp89exZRFDlw4AAajUZqtD5u3DgiIiJobGzk9ddfl9Ixixcv5vLly1y8eFEKzvemaoyMjCTrkhEjRpCWloarqytFRUVs3bqVxsZG+vTpw8svv4y+vj4TJ07k+PHjFBUV4eDgQHh4OLt27aJ///4/Sj9bkFf4LzyiKLJ9+3bKy8t55513MDIykrpdjRo16r4NyZ8zDQ0N1NXVSb493e6i3Xnd7gYr9vb23LhxQ9KWx8fHo1Qq+eUvf0lBQQGFhYWcPXuWSZMmMWzYMClPrlAopLQNwJo1a7h48aKkc++uCr5z5450DPy7CvTbCIKAsbGx1MAjLi7uvmPu7UDW/Zo+ffpIdxfDhw9n3LhxpKenc/nyZSorKyXde3fnpu7xnZ2dWbFiBXV1daxfvx4jIyMaGxsJCAhAoVDQp08f4uPjqaqqQkdHBx8fH1xdXbl8+TL19fVSA/luC4RZs2aRnJxMaWkpr7/+uiQXjYyMJD4+HkNDQ8nzB7ouGrq6uqxdu/ahiqkjR45Iaalu7k2pQFch086dO6WK6NLSUql/wM6dO7Gzs6O8vPyh3+/09HT27t2LSqXC3Nyct99+G+j6X/n88897XOgWLlxIRUUFycnJ+Pr6MmLEiB5zb29vp6qqCltbW8nDv7v24inydFb4giBYAnsBNyAPeEkUxdpvHRMIbAJMAQ3wZ1EU9z7JuDK9hyAITJs2jc8++4zo6GjGjh0rNXjIysp6rgK+qalpj1Wjs7MzlpaWpKamYm5ujqWlJYWFhVIjdB0dHS5fvgx0pSvu3LnDsWPHEASB1atXS/seoaGhtLW1kZqaSmVlJZ6enmRmZpKVlcXEiRPp06cPISEh7N27l6SkJBwcHBg+fLhkmVBRUQEgqTa6JaharZbGxkYAEhISHmgxrauri1qtxsvLi9LSUurq6qRgb2RkhKenJ+vWrZM2R83MzHBxcZH094DU+CM0NJSIiAgyMzOlsQcPHkx+fj6VlZXSxSUgIIDa2lpu375NVVWVVE/QvUrv7i97/PhxKZjHxMQwe/ZsRFGkuroarVYraf/Pnz9PXV0dBgYGNDc3ExkZiaurK66urj3083V1ddy+fZuQkBA8PDwQRZHMzEzi4uIICgrCzs6O5ORkTp48iUaj4aWXXkJfX59t27bh6+uLo6MjQUFBVFdXExgYyOjRox/4PenuXTt48GCuXbtGTU0NN27ckGobwsPDiY2NlWy/fXx8HnouPT29Hlbf994x/Bg80QpfEIT/A2pEUfxfQRB+A1iIovj/vnWMFyCKopgpCIIDkAD4iqJY913nllf4z5bo6GhiY2OlVaqvry+3b9/mgw8+eGD/1OeF7pV2tyyvWwpqYWGBIAi0tLRQX1/P7t27aWxslHTe3YVd93L06FFSUlL4xS9+wdatWzExMeGVV15Bo9FI+nI9PT0SExNxcnKSNpoLCgpITU1l+PDhUn9UXV1dZs2axbFjx1CpVD3ULHZ2drS3t2NiYiIF2XurlXV0dBgwYACJiYkoFAosLS0JDw+ntLSUy5cv09nZKbWbNDIyorOzEwcHB6qrq6WmH+7u7pLEsb6+nlGjRknFRvn5+ZJBXWFhIRMmTCAnJ4ecnBy8vLzw8PDg6tWr1NXVAUjFcN29BLKzs+9L7QwaNIhp06bxxRdfSCtolUrF/PnzcXR0xNjYWLKaXrt2LWZmZkDXftT69esxNzdn9uzZbN68GQcHB2bOnImVlRVqtZpt27ZRXFyMjo4OS5YsQU9PT2pj6O7u3kM6qdFo2LhxI8bGxowdO5YdO3ZgZWVFdXU10LXJvGbNGsrLy2lra/vJFDB+i6eWw58FjP3Xz9uBC0CPgC+K4t17fi4RBKECsAHqnnBsmV5k9OjR1NbWYmFhQWBgoKSyyM3NlTxknrdNXeA+/XV3wU43hoaGGBoasmTJEk6dOsW4cePYt28fqampGBgYUFlZSXBwMM3Nzdy+fZugoCAMDAzw8PAgLi6Ojo4Orl27RkZGBhkZGZLypbtC1MjICBcXFynNNHHiRHbu3MmkSZPw8/PDz8+P5uZmjh49SmZmJubm5ixbtkxyGW1qauLWrVtERUVJq3+lUim1gNRqtbi7u2NtbY2xsbF00YmMjKSsrAw7Ozusra25evUqgiAwZMgQKT2i1WqJjo7GysqKsWPHMnbsWKn24fTp0yxbtoyioiK8vb0ZOnQoBQUFkldTcHAwly5dQqFQMGLECL744gvJZ0ehUJCWlibNddq0aQQGBkoprPLycsaPH8+5c+fYs2cPdnZ2LFiwgISEBAICAqRgD113RTNnzmTPnj1s3LgRlUrF3Llzqaurw8zMjPT0dIqLiwkJCSEnJ4edO3f2SKfZ2toye/Zsjhw5gqurK8bGxtTU1BAeHo6joyOCIFBdXc3IkSMJCgpCV1dXUj39HHnSgG8nimLpv34uA+y+62BBEEIAXSD7Ic+vAlYB9zULkHm66OrqsmDBAul3rVaLvr4+cXFxnD59Gmtra6ZPn/6zlG/2BnZ2dlLjDG9vb1JSUkhLS0OtVlNRUUFNTQ0ajUayofb09JRy+9353ZqaGgoKCvDx8SE9PZ3k5OT7iqxsbW1xc3PrcdEpKyvDxcWF4OBgnJ2d0dXV5fTp0/+/vTOPqupKE/1vX2aJCirDjSCDIo4IggoaFQfiGKVTloWlJnaZGGPs1KqqrNXplX96vbfee+leK+lUVazVsTpJGysmKg4Bo0k5oKiIgCPKIDKIIKCMiggXuLv/uPeed1EQlcug7N9arHvO3vuc893vHL67z7f3/j4mTpyIr68vkZGRnDt3jurqai3RuiVoWmBgIOnp6W38/1FRUdpq44KCAoKDg7VVs2lpaYSGhqLX65kwYQLJycl4eXlRXFzMgwcPNDdPRkYGGRkZREdHA2j5dMH07JSWlhIdHa11EtasWcP27du5f/8+vr6+FBUVaeEjbt26RVhYGM3NzZSWlmJnZ8fx48e1YysqKti9ezc6nY45c+YApvEWe3t7LSeARX4nJyfq6+s1N055eTkDBw5k4cKF1NfXs2/fPry9vZk2bRqlpaUkJCSwdetWAM21Nn78eG0xl16vp7GxkVmzZvXZhDFPQ6cGXwhxBPBup+oj6x0ppRRCdOgfEkLoge3Am1JKY3ttpJRbga1gcul0Jpui+7AEK7P4ty2hBN59911bxft4brEs7R8yZAh+fn6kp6djb2/PwoULtZgpI0aMwNnZmfPnz+Ph4cGSJUswGAxcunSJV155hW3btnHhwgXCwsLaDPKdP3+ewsJCSkpKWL16NUOHDiU+Pp7GxkYtYUdSUhLp6enk5+ezadMmjh8/rk2NHDBgAPb29ly7dg29Xk90dDRVVVXY29vj4eGBTqfjzJkzACxZsoQff/yxTfA3nU7H0aNHWbNmDcnJyRgMBrKysrRE6QMHDmTw4MG4uLiQnJyMv78/J06cwNfXVxvvOXr0KCkpKcTExDB8+HAOHjzI0KFDtRALwcHBfPLJJ0RGRnL//n1tULy4uJjGxkZef/11iouLyc/Pp6amRuv1BwcHU1JSQlJSElVVVQwaNIj169fz448/aj8O9+/f17KBWd4i7O3tOXPmDBERESxYsIC0tDQSExOJi4tjw4YN7N69mzt37tDa2oqbm1ubFa6/+tWv0Ol0L4Sxh6778HOBaCllmdmgH5dSPhLQWQgxCJO75/9KKeOf5NzKh9/7FBcXk5GRwYIFC2hpaeEvf/kL/v7+rFq1qrdF61WMRiMZGRkEBwczaNAgsrKy8PHxaeNqANOsICGElv/XGks8FTDl8V2+fDlSSv70pz/h6upKU1MT1dXVeHh4UFlZiaurK05OTsycOZN9+/bh5eVFeXk5/v7+FBUVERoaqvn+BwwYQE5ODnPnzuXSpUs0Njbi5uam9Z4tg9erV6/m448/RqfTsXjxYqqqqkhJSUFKSXBwsJZO0hJ22hJ9tKWlRQv/bM1bb73F3bt32bVrF05OTjQ3N2uDtmByv0RERFBZWUl2djbvvvsuQ4cOJTExsc3Mm4iICJYsWUJrayt//vOfqa+vx9HRUQuzAKaQGRUVFfj4+GjjGAEBARQWFj4yW8oSlM6C5W1g6dKljBkzhk8//VST6/bt2/z2t7/tMNSCBSklra2tnbZ7mEuXLjF06NAupUx8ArrNh58AvAl8bP784ZErC+EI7AO+eVJjr+gbWPuWweTnP3LkCHl5ec+c8u1FQKfTaSF7gUeW61toL+SChUmTJjFw4EAyMzO5ePGilkiltraWefPmMXLkSA4ePMiVK1eYPXs23t7e7Ny5k7179+Lu7s4bb7zBrl27tBjxS5cuJTk5mZMnT2quldTUVBoaGrSIoNXV1Rw4cIDCwkLCw8PJz8/HaDQSFxen3c8xY8awbds2zdj7+fmxYsUKzpw5Q3Z2Nh4eHkRHR6PX6/npp59IT0/Hz8+PwsJCvv76awBtINhi7BcvXkx2djaFhYWcPHlS84F7eHgghGDAgAEAxMbGUl5eTmpqKl5eXloU09bWVi0ZvIuLCy4uLkgpiYqKIiUlBSEEOp2O2bNnU1hYqLl2pk+fjr29PTNnzqSgoIDi4mIGDx7MqFGj+P777zl9+jQFBQUYjUYiIiKor6/nm2++IT09naioKMAUR6moqIi6ujqCgoIYNmwYzc3N7Nixgxs3buDt7Y2LiwtCCOzs7JgzZw7Dhg3jq6++YsqUKYSFhWn3/N69e/zwww94enryzjvvdDgmZlkb8riYSs9KV3v4Q4FdwAjgBqZpmdVCiAhgo5TyLSHEGuBr4KrVoeuklBcfd27Vw+97tLa2smXLFgYOHKj5sxVdo6WlhS1btmiD4g0NDfz+97/Xeo6VlZWamygrKwtXV1d8fX2xs7PTYsOHhIQghKCkpIQvv/wSMI0hNDQ0EBAQoKWBBNM93LNnD9nZ2Xh7e1NXV8cf/vCHNvPCm5qa2Lt3L2VlZWzYsOGxyTksUUC//fbbNlNGLSksLWM/iYmJtLS0sGnTJrZv367N1w8ODiYxMZEJEyYQGxtLa2sr3333Hfn5+Tg6OmJnZ8fUqVNpbm7Gy8uLoKAgrly5wsGDBxk7dqz2PYKDg5k9ezaff/45dXV1fPDBB48sxrLGMtceTAPlFuO6fft2ysrKeP/993nw4IG2oMqCJajezZs3CQ8Pp7q6mubmZqSU3L59W8s8ZnnLee+997Q3POucC+vWraO0tJQhQ4a0me1liacTFBREXFzcsy7QUsHTFLYhJSWFw4cPs3HjRry8HjtGr3hCLMbH09OTuXPnPnOaOykln332Ge7u7qxdu7bDxT1NTU188cUX1NTUEBYWxrJly9ptZwkc9yRUVVVx+PBhDAYDpaWlGAwGxo8fT15enpart6mpSZuiGRwcTH5+vhapcvPmzZpLzGg0cvToUa5evUpcXJwWWdNCY2Mjn3zyCS0tLYSHh7NkyRKtt5ydnc3du3c7zeEspSQhIQEfH59HVphv3boVvV5PQ0MDTU1NrFy5kiFDhpCZmalFSF20aNEjSU0OHTrEuXPn8PX1paKiAoPBwOjRo1m2bBlOTk58/vnnuLi4aGMq9fX1ODg4sHnzZlxcXLQFacHBwaxYseKp3UVWKIOvsA0NDQ18+umn2rxphW2or69vE3r5WWloaMDR0bFTY1FSUsKOHTtYtWoVvr6+XbommMYrvv32W+7cucOkSZPw8/MjJCSEuro6UlNTmTJlCsnJyWRmZmoujZaWFm22zcPB5zrDkiDekjvWlqSmppKZmYnBYGD58uWP+Ns7CqdsSZYDMG3aNFxcXDh+/Dh2dnZ4eHhQXl7O8uXLqaioIDU1VfvR0+v13Lt3j9raWqZNm0ZMTEy3JTFXBl/x1Ozbt4/s7GzCwsK0FY6K5w+LO6ar1NXVsW3bNhoaGvjlL3/ZYZ6Fe/fusWfPHubMmYOfn1+Xr9sX+eKLLygvL9eS9pSWlpKVlUVZWZmWLMdoNHL16lVCQ0M5ffo0SUlJeHp6smjRIvz9/W0hhjL4CttRXV1NQkICpaWlODs7s3Hjxhd6Na6iY27cuMGePXswGAysXbu2TRiB/si1a9fIzc1l6dKlT/RjajQaKSkpwcfHx5YB1ZTBV9ieiooK/vrXvxIYGEhsbKw220Lx4nP//n1OnDhBRkYGbm5urFy58hFfu6LXUAZf0T1YVpOCaUHS4sWLSUtLw9XVtc3URcWLQ3V1NV999RUNDQ2Eh4czf/78Xg8KpmiDioev6B4iIyPx8fEhJyeHlJQUcnJytHnQ4eHh3R0GVtFDSCm5dOmSFuHTaDTyzjvvqPGb5wxl8BVdxsfHBx8fH0aOHMmJEyfw9vbm7NmzFBUV9flE6YrOaWlpISEhQUuA4uzszOrVq5Wxfw5RBl9hMwICAggICKC5uZlz586Rm5urDP5zTnV1NfHx8ZSVlTF37lyioqK0VaWK5w9l8BU2x8HBgZEjR5Kbm8vUqVOpqqrC2dmZESNGvJAhll9EqqqqSEpKIicnBwcHh3bj/yueP5TBV3QLluBbW7Zs0cosCaQVfRspJXv37qWqqorJkyczffr0NsnRFc8vyuAruoVx48ZpwaV8fX3JyMggJSWFoKAgWy0uUXQTV65c4datW8TGxjJp0qTeFkdhQ5TBV3QLTk5OxMbGavseHh4UFxeTkJDA5s2bqauro7S0lPHjxys3Ty9TU1PDl19+SVBQEEFBQRw5cgRvb29CQkJ6WzSFjbHZ0i6F4nE4Ojoyd+5campqyM/PZ//+/ezZs6dNomtF73D69GkePHjA5cuX2b17N1LKNgHJFC8Oqoev6DHGjBmDq6srP/30E9XV1fj4+HDhwgUGDBjA/Pnze1u8fkl9fT0XL14kNDSUqKgoamtrCQwMtOUyf0UfQt1VRY9hZ2fH5MmTqa6uxtXVlTfeeIOQkBBSU1OpqakhLy9Py7Wq6F6klFqP3mg0MmPGDIYNG8aoUaOUsX+BUXdW0aNMnjwZe3t7ZsyYgYODA/PmzUMIwdatW9mxY4fmUlB0LwUFBezbt4/a2lpiYmL6fZ7i/oIy+Ioexc3Njd/97ndERkYCpjSAs2fPxmg0Mn78eIqLi7l69SrNzc1aTlJF15BSkpeXR2lpqVZmmV+/efNmLZ2f4sVH+fAVPc7DUTVfeeUVLcVcVVUV+/fvp7W1FQB3d3d+/etfP3WCDIWJe/fu8d1331FWVoajoyO/+c1v8PT01FZBOzg49LaIih5E9fAVfQKdTodOp2PZsmWMGzeO2bNnM2fOHJqamvj++++1JNaKp+PUqVNUVFSwePFinJyc2LFjB1lZWdy7d++ZUykqnl+UwVf0KfR6Pa+//jrR0dHMmjWLlStXUlNTQ2JiIgBJSUmkpaX1spTPB42NjVy4cIGJEycyZcoUVq1ahcFgID4+HiEEo0eP7m0RFT2Mcuko+jR+fn5ER0dz7NgxEhMTOX/+PM7OzkyePBkpJVJKHB0de1vMHsNgMNDS0vKIWyw9PZ3Dhw8DJpeZu7s7Li4uNDc3awm99Xo9GzZsID4+nsGDB6uENf0QZfAVfZ7p06eTmZnJ+fPneemll6ivryc7O5uzZ89SVVXFvHnzmDBhAs7Ozr0tardhNBo5dOgQly5dorW1lfnz5zNt2jR0Oh0FBQUcOnSIESNGoNfraWhooLy8nKKiIvz9/dHr9dp53N3defvtt9VMqH5KlzJeCSGGADsBf6AIWCmlrOmg7SAgC9gvpdzc2blVxiuFNaWlpRw+fJilS5eyfft2DAYDjY2NeHh4cOfOHQDGjx/PL37xC27evEl5eTlTpkx5blaL1tTU4O7u3mF9Xl4eO3bsYOLEiRgMBnJzc7G3t8fZ2Zn6+no8PDxYv369lnlKSsmdO3d46aWXVE++/9FtGa8+BI5KKT8WQnxo3v/nDtr+byC5i9dT9FOGDx/OunXrAAgJCeHUqVMEBgayZs0aioqKyMrKIiMjA29vb1JSUnjw4AE3btwgNja2z89Eyc/P529/+xuvvfYakydPBiA7O5vKykpmzJiBTqfTViQvX74cnU5HTk4OxcXFPHjwgGHDhjFp0qQ2aQaFEHh6evbWV1L0Ubpq8JcD0ebtbcBx2jH4QohwwAv4CYjo4jUV/ZyIiAhu3bqlxXsJCAjA39+f8vJyjh49ir29PdOnTyclJQWj0cjKlSsf6ekXFhZy4cIFFi9e3OuuIEsmqZ9//pmAgADs7e3Zv38/BoOBkpISYmJitNwClsQjY8eOZezYsb0ptuI5pKuzdLyklGXm7XJMRr0NQggd8AnwQWcnE0JsEEJkCCEyLK/pCsXDDB48mLVr17ZZHSqEYOnSpbi4uLBo0SJiYmJYuHAhOTk5/P3vf0dKidFopK6ujoqKCnbu3ElmZibx8fEdBm9rbm4mLS2tWxaAWVwuLS0t5OTkEBgYCMCOHTu0dQgzZ84kLy+PLVu2YDQaCQsLs7kciv5Fpz18IcQRwLudqo+sd6SUUgjR3oDAJuCglLKkM3+qlHIrsBVMPvzOZFMorPHy8uKDDz7QYsFMmzaN6upqUlNTaWhooLKyklu3bgHg6upKVFQUx48fZ//+/SxdupT8/Hxu376NEILIyEiSk5M5ffo0RqNRWxkMJmN98+ZNXn75Zezt//+/UGtrK1euXKGiogInJydmzZqlvVmkpaVRW1uLp6cnISEhHDt2jNOnTzNy5EiampqIjIzEzs6OhIQECgoKeOWVV5g7dy4TJkzg7Nmz2NnZKReNost0avCllB2GMRRCVAgh9FLKMiGEHrjdTrMoYKYQYhPwEuAohKiXUn74zFIrFB3wcOCvhQsX4ujoyKlTp7SonC0tLYwbNw4PDw+EECQlJZGdnd2mJ5+fn6+FIjh79ixTp07Vzp2Zmcm+ffsIDQ1l2bJl5OXlUVZWRmZmJlVVVeh0OoxGI35+fvj7+1NbW8uhQ4cQQiClJDU1lYqKCgYNGkR+fj7Ozs4EBgZiZ2fHe++9x/Xr1wkKCgLA09OT1157rYe0p3jR6aoPPwF4E/jY/PnDww2klKst20KIdUCEMvaKnkIIwbx58xg1ahTDhg3D1dW1Tf2sWbPw9vbm3LlzTJo0ieDgYC5fvkxCQgKOjo68+uqrHDp0iCNHjnD//n18fX05duwYjo6OXLx4kcrKSkpKSgCTcY6LiyMwMJDPPvuMs2fP4u/vz/nz5xFC8P7771NcXMyBAwfQ6/WsW7eOpKQk3NzcNN+8g4OD8s0ruo2uGvyPgV1CiPXADWAlgBAiAtgopXyri+dXKGyCn59fh3WjR49us+o0LCwMBwcHred95swZzpw5g4ODA5cvX8bOzo63336bAwcOcOvWLWJiYpgyZUqb2UDh4eGcPHmSO3fucOHCBYKCgnBzc8PNzU2LYePo6MiCBQu69XsrFNZ0aR5+d6Lm4Sv6ChUVFdy9e5eRI0dSUFCATqcjMDCQpqYmGhoa2p0/f+/ePf74xz9qQeBWrVqlQhkoeooOB0uVwVcouonS0lJyc3Npbm4mJiZGJRZR9BTdtvBKoVB0wPDhwxk+fHhvi6FQaKguh0KhUPQTlMFXKBSKfoIy+AqFQtFPUAZfoVAo+gnK4CsUCkU/QRl8hUKh6Ccog69QKBT9BGXwFQqFop/QZ1faCiHuYIrP86wMAyptJI4tUXI9HUqup0PJ9XS8iHJVSikXtlfRZw1+VxFCZEgp+1x2LSXX06HkejqUXE9Hf5NLuXQUCoWin6AMvkKhUPQTXmSDv7W3BegAJdfToeR6OpRcT0e/kuuF9eErFAqFoi0vcg9foVAoFFYog69QKBT9hOfa4AshfimEuCqEMJrz6HbUbqEQIlcIcV0I8aFVeYAQ4qy5fKcQwtFGcg0RQhwWQuSZPx/JgSeEmCOEuGj11yiEiDXX/bcQotCqLrSn5DK3a7W6doJVeW/qK1QIccZ8vy8LIX5lVWczfXX0rFjVO5m/+3WzLvyt6v7FXJ4rhLBpstonkOv3Qogss26OCiH8rOravZ89KNs6IcQdKxnesqp703zf84QQb/agTP9hJc81IUStVV236UsI8ZUQ4rYQ4koH9UII8Sez3JeFEJOt6rquKynlc/sHjAWCgeNARAdt7IB8IBBwBC4B48x1u4A48/Z/Au/aSK5/Bz40b38I/Fsn7YcA1cAA8/5/Ayu6QV9PJBdQ30F5r+kLGA0EmbdfBsoAN1vq63HPilWbTcB/mrfjgJ3m7XHm9k5AgPk8djbSz5PINcfq+XnXItfj7mcPyrYO+LydY4cABeZPd/O2e0/I9FD7fwK+6iF9zQImA1c6qF8MHMKUpjASOGtLXT3XPXwpZbaUMreTZlOB61LKAimlAfgeWC6EEMBcIN7cbhsQayPRlpvP96TnXQEcklI22Oj6HfG0cmn0tr6klNeklHnm7VvAbcDDRte30O6z8hhZ44F5Zt0sB76XUjZJKQuB6+bz9YhcUsokq+cnFfCx0bW7LNtjWAAcllJWSylrgMNAuytEu1mmVcB3Nrhup0gpkzF17jpiOfCNNJEKuAkh9NhIV8+1wX9ChgM3rfZLzGVDgVopZctD5bbAS0pZZt4uB7w6aR/How/c/zG/0v2HEMKph+VyFkJkCCFSLW4m+pC+hBBTMfXc8q2KbaGvjp6VdtuYdVGHSTdPcuyz8rTnXo+pl2ihvftpK55Utl+Y70+8EML3KY/tLpkwu74CgGNWxd2pr87oSHab6KrPJzEXQhwBvNup+khK+UNPy2PhcXJZ70gppRCiw7mv5l/vicDPVsX/gsnwOWKaj/vPwP/qQbn8pJSlQohA4JgQIhOTYXtmbKyv7cCbUkqjufiZ9fWiIYRYA0QAs62KH7mfUsr89s/QLSQC30kpm4QQ72B6Q5rbg9d/HHFAvJSy1aqst/XVbfR5gy+lnN/FU5QCvlb7PuayKkyvS/bmnpqlvMtyCSEqhBB6KWWZ2UDdfsypVgL7pJTNVue29HabhBBfAx/0pFxSylLzZ4EQ4jgQBuyhl/UlhBgE/Ijpxz7V6tzPrK+H6OhZaa9NiRDCHhiM6Vl6kmOflSc6txBiPqYf0NlSyiZLeQf301YGrFPZpJRVVrv/hWnMxnJs9EPHHu8JmayIA96zLuhmfXVGR7LbRFf9waWTDgQJ0wwTR0w3OEGaRkKSMPnPAd4EbPXGkGA+35Oc9xH/odnoWfzmsUC7I/rdIZcQwt3iEhFCDANmAFm9rS/zvduHyb8Z/1CdrfTV7rPyGFlXAMfMukkA4oRpFk8AEASkPaMcTy2XECIM+AJYJqW8bVXe7v20kVxPKpveancZkG3e/hl41SyjO/Aqbd90u00ms1xjMA2AnrEq6259dUYC8IZ5tk4kUGfu0NhGV901Gt0Tf8A/YPJlNQEVwM/m8peBg1btFgPXMP1Kf2RVHojpn/I6sBtwspFcQ4GjQB5wBBhiLo8A/suqnT+mX27dQ8cfAzIxGa6/AS/1lFzAdPO1L5k/1/cFfQFrgGbgotVfqK311d6zgsk9tMy87Wz+7tfNugi0OvYj83G5wCIbP+udyXXE/D9g0U1CZ/ezB2X7f8BVswxJwBirY39j1uV14B97Sibz/r8CHz90XLfqC1Pnrsz8LJdgGm/ZCGw01wtgi1nuTKxmH9pCVyq0gkKhUPQT+oNLR6FQKBQog69QKBT9BmXwFQqFop+gDL5CoVD0E5TBVygUin6CMvgKhULRT1AGX6FQKPoJ/wPfxxhEsEy96AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_o_t, x_o_x = create_t_x(theta_o)\n",
    "plt.plot(x_o_t, x_o_x, \"k\", zorder=1, label=\"truth\")\n",
    "\n",
    "theta_p = posterior.sample((10,), x=x_o)\n",
    "x_t, x_x = create_t_x(theta_p.numpy())\n",
    "plt.plot(x_t, x_x, \"grey\", zorder=0)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The functions are a bit closer to the observation than prior samples, but many posterior samples generate activity that is very far off from the observation. We would expect `sbi` do better on such a simple example. So what's going on? Do we need more simulations? Feel free to try, but below we will show that one can use the same number of simulation samples with different summary statistics and do much better."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.5.2 Using 3 coordinates as summary statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = get_3_values(theta.numpy())\n",
    "x = torch.as_tensor(x, dtype=torch.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Neural network successfully converged after 127 epochs."
     ]
    }
   ],
   "source": [
    "inference = SNPE(prior)\n",
    "\n",
    "_ = inference.append_simulations(theta, x).train()\n",
    "posterior = inference.build_posterior()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The observation is now given by the values of the observed trace at three different coordinates:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_o = torch.as_tensor(get_3_values(theta_o), dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3cbb37d1e71544d9a5b2418b13809383",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Drawing 10000 posterior samples:   0%|          | 0/10000 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x504 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta_p = posterior.sample((10000,), x=x_o)\n",
    "\n",
    "fig, axes = pairplot(\n",
    "    theta_p,\n",
    "    limits=list(zip(prior_min, prior_max)),\n",
    "    ticks=list(zip(prior_min, prior_max)),\n",
    "    figsize=(7, 7),\n",
    "    labels=[\"a\", \"b\", \"c\"],\n",
    "    points_offdiag={\"markersize\": 6},\n",
    "    points_colors=\"r\",\n",
    "    points=theta_o,\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "80f75d8aa7ea407dba7a3eb0cead846a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Drawing 100 posterior samples:   0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f82885b4af0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_o_x, x_o_y = create_t_x(theta_o)\n",
    "plt.plot(x_o_x, x_o_y, \"k\", zorder=1, label=\"truth\")\n",
    "theta_p = posterior.sample((100,), x=x_o)\n",
    "ind_10_highest = np.argsort(np.array(posterior.log_prob(theta=theta_p, x=x_o)))[-10:]\n",
    "theta_p_considered = theta_p[ind_10_highest, :]\n",
    "x_x, x_y = create_t_x(theta_p_considered.numpy())\n",
    "plt.plot(x_x, x_y, \"grey\", zorder=0)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok this definitely seems to work! The posterior correctly focuses on the true parameters with greater confidence. You can experiment yourself how this improves further with more training samples or you could try to see how many you'd exactly need to keep having a satisfyingly looking posterior and high posterior sample simulations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, what's up with the MSE? Why does it not seem so informative to constrain the posterior? In 1.6, we'll see both the power and pitfalls of summary statistics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.6 Prior simulations' summary statistics vs observed summary statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to understand this...Let's look at a histogram of the four summary statistics we've experimented with, and see how they compare to our observed truth summary statistic vector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x216 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stats = np.concatenate(\n",
    "    (get_3_values(theta.numpy()), get_MSE(theta.numpy(), theta_o)), axis=1\n",
    ")\n",
    "x_o = np.concatenate((get_3_values(theta_o), np.asarray([[0.0]])), axis=1)\n",
    "\n",
    "features = [\"y @ x=-0.5\", \"y @ x=0\", \"y @ x=0.7\", \"MSE\"]\n",
    "fig, axes = plt.subplots(1, 4, figsize=(10, 3))\n",
    "xlabelfontsize = 10\n",
    "for i, ax in enumerate(axes.reshape(-1)):\n",
    "    ax.hist(\n",
    "        stats[:, i],\n",
    "        color=[\"grey\"],\n",
    "        alpha=0.5,\n",
    "        bins=30,\n",
    "        density=True,\n",
    "        histtype=\"stepfilled\",\n",
    "        label=[\"simulations\"],\n",
    "    )\n",
    "    ax.axvline(x_o[:, i], label=\"observation\")\n",
    "    ax.set_xlabel(features[i], fontsize=xlabelfontsize)\n",
    "    if i == 3:\n",
    "        ax.legend()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that for the coordinates (three plots on the left), simulations cover the observation. That is: it covers it from the left and right side in each case. For the MSE, simulations never truly reach the observation $0.0$.\n",
    "\n",
    "For the trained neural network, it is strongly preferable if the simulations cover the observation. In that case, the neural network can **interpolate** between simulated data. Contrary to that, for the MSE, the neural network has to **extrapolate**: it never observes a simulation that is to the left of the observation and has to extrapolate to the region of MSE=$0.0$. This seems like a technical point but, as we saw above, it makes a huge difference in performance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.7 Explicit recommendations\n",
    "\n",
    "We give some explicit recommendation when using summary statistics\n",
    "\n",
    "- Visualize the histogram of each summary statistic and plot the value of the observation. If, for some summary statistics, the observation is not covered (or is at the very border, e.g. the MSE above), the trained neural network will struggle.\n",
    "\n",
    "- Do not use an \"error\" as summary statistic. This is common in optimization (e.g. genetic algorithms), but it often leads to trouble in `sbi` due to the reason above.\n",
    "\n",
    "- Only use summary statistics that are necessary. The less summary statistics you use, the less can go wrong with them. Of course, you have to ensure that the summary statistics describe the raw data sufficiently well."
   ]
  }
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